A    CONTINUATION 


DE  DAMOISEAU'S  TABLES 


SATELLITES  OF  JUPITER, 


TO 


THE  -YE 


19OO 


D.  P.  JODD,  B.  A. 


PUBLISHED  FOR  THE  AMERICAN  EPHEMERIS  AND  NAUTICAL  ALMANAC, 
BY  AUTHORITY  OF  THE  SECRETARY  OF  THE  NAVY. 


WASHINGTON: 

BUREAU   OF   NAVIGATION. 

1876. 


Tb 


PREFATORY  NOTE. 


THE  Tables  Ediptiques  des  Satellites  de  Jupiter,  d'apres  la  Theorie  de  leurs  attractions 
mutuelles  et  les  constantes  deduites  des  Observations,  par  le  Baron  DE  DAMOISEATJ,  Paris, 
1836,  terminate  with  the  epoch  1880.0.  Entirely  new  tables  of  the  satellites,  being  very 
laborious  to  construct,  have  not  yet  been  published.  .In  this  continuation  of  the  Tables 
Ediptiques,  no  changes  in  the  fundamental  formulae  and  elements  have  been  made,  it  being 
believed  that  the  consequent  inconvenience  to  the  future  investigator  of  the  motions  of  the 
satellites  would  more  than  neutralize  any  advantages  supposed  to  arise  from  such  a  change. 

The  work  was  planned  early  in  the  present  year :  the  definitive  computations  were 
not,  however,  commenced  until  August. 

An  acknowledgment  of  indebtedness  is  due  Professor  NEWCOMB,  from  whom  advice 
has  been  received,  from  time  to  time,  during  the  prosecution  of  the  work. 

D.  P.  TODD. 

WASHINGTON,  1876,  November  the  1th. 


CONTENTS. 


INTRODUCTION. 

THE  CONSTRUCTION  OF  THE  TABLES. 

THE    FIKST    SATELLITE. — Table  I,  the  epochs  of  the  mean  conjunctions 

The  terms  of  the  arguments  of  the  inequalities  which  increase  uniformly  with  the  time 7 

THE  SECOND  SATELLITE. — Table  I,  the  epochs  of  the  mean  conjunctions  .. 

The  terms*  of  the  arguments  of  the  inequalities  which  increase  uniformly  with  the  time 8 

THE    THIRD   SATELLITE. — Table  I,  the  epochs  of  the  mean  conjunctions 

The  terms  of  the  arguments  of  tin-  inequalities  which  increase  uniformly  with  the  time 8 

THK  FOURTH  SATELLITH.— Table  I,  the  epochs  of  the  mean  conjunctions 

The  terms  of  the  arguments  of  the  inequalities  which  increase  uniformly  with  the  time 9 

The  formation  of  the  complete  arguments  of  the  inequalities  of  the  satellites . .  .. 9 

THE  FORMATION  OK  TABLE  III.— Terms  in  ( J  +  <j>  +  6 E  ) 'J 

Tabular  values  of    J,     J  +  0,     Qt  +  fr,     (!E .' 9 

The  mean  sviioilic  revolutions  of  the  satellites,  expressed  in  days 10 

Terms  in  (5  it  —  2«0) 10 

Terms  in  (n  —  A,,),      (  II  —  A,,,  )}  etc 11 

Comparison  of  Table  III  with  Dn  DAMOISEAU 

Longitudes  of  Observatories  from  Paris. .. 

The  continuation  of  the  tables  of  the  configurations. . 

Values  of  the  motion  of  «,,    «„,    «,„,    «|V.  in  3!>T>  and  :{fi(i  (lays 

Adopted  values  of  ?/,,    «n,    «,„,    «lv.  lf*0,  January  1.  i'aris  mean  midnight 

Errors  in  IM.  OAMOISK.AU'S  Tulles  Ecliptiquet,  tie... 

TABLES— 

OK   THE    ECLIPSES. 

THE     FIRST    SATK.LLITE. — Table      I,  Epochs  of  the  mean  conjunctions  and  the  arguments  of  the  inequalities ,.,, 16 

Table  III,  1'erturbations  of  Jupiter  and  other  inequalities 18 

THE  SECOND  SATELLITE. — Table  I,  Epochs  of  the  mean  conjunctions  and  the  arguments  of  the  inequalities 20 

Table  III,  Perturbations  of  Jupiter  and  other  inequalities 22 

THE  THIRD  SATELLITE. — Table  I,  Epochs  of  the  mean  conjunctions  and  the  arguments  of  the'  inequalities 24 

Table  111,  Perturbations  of  Jupiter  and  other  inequalities 2C 

i'HK.  FOURTH  SATEI.I.ITK. — Table  I,  Epochs  of  the  mean  conj unctions  and  the  arguments  of  the  Inequalities 28 

Table  III,  Perturbations  of  Jupiter  and  other  inequalities 30 

Table  A,  Longitudes  of  Observatories  from  Paris 

OK  THE   CONKJGUKATlONS. 

THE     FIRST    SATELLITE. — Table  I,  Epochs  of  the  mean  longitude  mid  the  arguments  of  the  inequalities 34 

THE  SECOND  SATELLITE. — Table  I.  Epochs  of  the  mean  longitude  and  the  arguments  of  the  inequalities 35 

THE    THIRD    SATELLITE. — Table  T.  Epochs  of  the  mean  longitude  and  the  arguments  of  the  inequalities 36 

THE  FOURTH  SATELLITE. — Table  I.  Epochs  of  the  mean  longitude  and  the  arguments  of  the  inequalities 37 

Corrections  to  the  Tulles  ^cUptiquei  i?r«  Ki/rllitc*  </<•  Jupiter,  etc.,  par  le  Jiaron  l)n  TUMOISKAU,  I'aris,  IMIMi 38 


ranVBBSITY 
V^TFnW 


INTRODUCTION. 


THE  CONSTRUCTION  OF  THE  TABLES. 

THE  fundamental  formulae  and  elements  of  the  Tables  £diptiques  are  given  by  DE  DAMOISEAU,  Introduction, 
pages  (i)— (x). 

THE  TABLES  OF  THE  ECLIPSES.  —  Of  the  Tables  for  computing  the  eclipses,  those  which  require  extension 
are  I  and  III  of  each  satellite. 

THE  FORMATION  OF  TABLE  I. 

The  First  Satellite. —  Counting  from  the  first  mean  conjunction  in  each  year,  and  letting  i  represent  tho 
number  of  mean  synodic  revolutions,  then 

from  1750  to  1880,        i  =  26827 ; 
1880  to  1900,        i  =    4128. 

The  epoch  of  the  first  mean  conjunction  in  the  year  1880  is  January  1,  181'  16'"  45S.070,  Paris  mean  civil 
time. 

d       h        m        s 

The  mean  synodic  revolution  of  I  X  206  =  364  14  11  24.74721 

X  207  =  366     8  40     0.69259 

The  terms  of  the  arguments  of  the  inequalities  which  increase  uniformly  with  the  time  are  based  on  the 
data  of  the  following  table  : 

Argument. 


5 
tt 

1 
S 

9 

I 
II 

III 


Terms. 

"o   *o 

U  — ^' 

U  —  U0    —  7°-43 

«,— wn    _2°.77 

M,  —  «HI  —4°.  10 
«i  — *ni  — 5°.51 
«i  — TIV  — 5°.51 

M,   2tln  +7Tm 

M,  _2Mn+^T 

M,  —  n  —  5°.51 
«i  —An  —  5°.51 
«i  — Am  — 5°.51 


Adopted  value  for  first 
mean  conj.  1880. 

11  8?4926 

11  29.9085 

9  12.4537 

4  23.9896 


4 

1 


6.0301 
20.2086 
2  12.4348 
7  28.0372 


7 
I 


5.5824 
0.2171 


0  11.7738 
4  22.1023 


Motion  for 
i  =  206. 

30?2924 
359.3412 
329.0501 
149.9562 

44.9342 

27.6958 

29.5979 

272.2184 

270.3145 
30.2944 
42.3512 

32.8438 


Motion  for 
i  =  207. 

30?4395 

1.0856 

330.6474 

330.6841 

316.0261 
27.8302 
29.7416 

273.5399 

271.6267 
30.4415 
42.5568 
33.0032 


The  Second  Satellite. —  Counting  from  the  first  mean  conjunction  in  each  year, 

from  1750  to  1880,         i  =  13360; 
1880  to  1900,        i  =    2055. 
The  epoch  of  the  first  mean  conjunction  in  the  year  1880  is  January  3,  5'1  3'"  28.719,  Paris  mean  civil  time. 

The  mean  synodic  revolution  of  II  X  102  =  362  12  25  20.99381 

X  103  =  366     1  43  14.72904 


8 


INTRODUCTION. 


The  terms  of  the  arguments  of  the  inequalities  which  increase  uniformly  with  the  time  arc  based  on  the 
data  of  the  following  table : 

Argument. 


1 

a 
:i 
4 

5 


I 

II 
III 
IV 


Terms. 

Adopted  value  for  first 

Motion   for 

Motion  for 

nieiiii  foiij.  I--H. 

i  =  102. 

i  =  103. 

S.             o 

o 

o 

MO  

7T0 

11      8.6129 

30.1201 

30.4154 

U  — 

K' 

0      1.3362 

357.2974 

0.8003 

U  — 

MO     —  7M3 

9    13.7591 

327.1786 

330.3862 

MII  — 

Mm  —  2°.78 

1    24.5665 

149.1032 

330.5650 

«H- 

7Tni     —  5°.  51 

1    20.0917 

27.5365 

27.8065 

MH  

_                    FLO   r  i 
"IV      —  i>    .*}  1 

2    12.5521 

29.4296 

29.7181 

MI  

•4Wu    1    I'm 

7    29.1189 

270.6701 

273.323H 

MI  — 

"'  0/             1       JT 

7      6.6546 

268.7771 

271.4121 

Mn  — 

n    —  5°.5l 

1      0.3335 

30.1221 

30.4174 

MII  — 

A,,  —  5°.51 

0    11.9208 

42.1103 

42.5231 

Mn  — 

Anl—  5°.51 

4    22.2343 

32.6570 

32.9772 

Mn  — 

Alv  —  5°.51 

5      5.3055 

30.8085 

31.1105 

The   Third  Satellite. —  Counting  from  the  first  mean  conjunction  in  each  year, 

from  1750  to  1880,         i  =  6625 ; 
1880  to  1900,        i  =  1019. 
The  epoch  of  the  first  mean  conjunction  in  the  year  1880  is  January  4,  81'  27'"  5".256,  Paris  mean  civil  time. 

The  mean  synodic  revolution  of  III  X  50  =  358    7  39™  52*70985 

X  51  =  365  11  39  28.56405 
X  52  =  372  15  39     4.41825 

The  terms  of  the  arguments  of  the  inequalities  which  increase  uniformly  with  the  time  arc  based  on  the 
data  of  the  following  table  : 


Argument. 

Terms. 

Adopted  value  for  first 
mean  conj.  1880. 
s.        o 

Motion   for 
t  =  50. 

o 

Motion   for 
o 

Motion   for 
o 

t 

M    —  T0 

11 

8.7077 

29 

.7713 

30.3667 

30.9622 

2 

U  —  *' 

0 

2. 

4625 

353 

.1596 

0.2228 

7.2860 

S 

U    —  M0 

—  7°.43 

9 

14.7905 

323.3896 

329.8574 

336.3252 

4 

MU  —  Mm 

—  5°.60 

3 

20.0286 

294 

.7529 

300.6479 

306.5430 

5 

Mm  —  «iv 

—  3° 

.20 

9 

17. 

5541 

220 

.4407 

66.4496 

272.4584 

O 

1lm  —  Ttm 

—  5° 

.51 

1 

20. 

1813 

27 

.2177 

27.7620 

28.3064 

t 

Mm  —  TIV 

—  5° 

.51 

2 

12. 

6504 

29 

.0888 

29.6706 

30.2523 

8 

«,  —  2wn 

+  *i 

ii 

7 

29. 

9752 

267 

.5356 

272.8863 

278.2370 

9 

Af                               O  I/ 

H|               >%'£('][ 

+  7T, 

r 

7 

7. 

5018 

265.6644 

270. 

9777 

276.2910 

I 

«,„  —  n 

—  5° 

.51 

1 

0. 

3216 

29 

.7724 

30.3679 

30.9633 

II 

Mm  —  Am 

—  5° 

.51 

4 

22. 

3401 

32 

.2768 

32.9244 

33.5700 

III 

Mm  —  AIV 

—  5° 

.51 

5 

5. 

4064 

30.4517 

31. 

0608 

31.6698 

IV 

Mm  —  AH 

—  5° 

.51 

0 

11. 

9448 

41 

.6217 

42.4511 

43.2865 

The  Fourth  Sale/lite. —  Counting  from  the  first  mean  conjunction  in  each  year, 

from  1750  to  1880,         i  =  2834; 
1880  to  1900,        i  =    436. 
The  epoch  of  the  first  mean  conjunction  in  the  year  1880  is  January  1,  31'  C'"  37s. 286,  Paris  mean  civil  time. 

The  mean  synodic  revolution  of  IV  X  21  =  351  19  47  25.49492 

X  22  =  368  13  52  32.42325 


INTRODUCTION. 


Tlic  terms  of  the  arguments  of  the  inequalities  which   increase  uniformly  wilh  the  time  are  based  on  the 
data  of  the  following  table  : 


Argument. 

1 

9 
8 
4 

5 

6 

7 
I 

II 
III 
IV 


Terms. 

«„     3T0 

U    —  TT' 

U   ._Mo    —  7°.43 

«in  —  «iv  —  7°.40 
7,,,  _MIV  —20°.  50 

i/  P»°    f>Q 

(I'jy •  7T|y     —  -  «J     .»^O 

Miv_ffm  _  5°.53 

MIV  — n     —  6°.36 

«IV  — AIV.  —  6°.36 

MIV  —  Am —  6°. 36 

MIV  —  AH  — •  6°. 36 


Adopted  value  for  first 

INCMII   COIIJ.    1880. 

iT  8?4401 

11  29.2893 

9  11.8840 

6  10.7138 

4  8.7027 
2  12.3656 
1  19.9755 
0  29.3739 

5  4.3479 
4  21.2573 
0  10.8496 


Motion  for 
t  =  21. 

29?2317 
346.7584 
317.5280 

33.7389 

356.8882 
28.5616 
26.7248 
29.2341 

29.9003 
31.6942 

40.8682 


Motion  for 
i  =  22. 

30°6237 

3.2707 

332.6484 

155.3456 

253.8829 
29.9216 
27.9974 
30.6262 

31.3241 
33.2035 
42.8144 


which  is 


>  Longitude. 


The  remaining  terms  of  the  arguments  depend  on  J,  the  great  inequality  of  Jupiter  ;  and  on  < 
employed  by  DE  DAMOISEAU  to  represent  "  les  perturbations  en  longitude  "  of  Jupiter. 
Let  there  be 

<.'-,      the  sum  of  the  equations  from  BOUVARD'S  Tables*  XIII — XXVI, 

-k,    the  sum  of  the  constants  added  to  these  tables. 

V'i,     the  sum  of  the  equations  from  BOUVARD'S  Tables  XXVIII — XXXVI,  \  T>  j-        ector 

-'&!,  the  sum  of  the  constants  added  to  these  tables. 
I  then  understand  from  DE  DAMOISEAU,  Introduction,  page  (ni),  that 

<4  =  4'  —  1'k, 

that  is,  the  "perturbations  in  longitude"  (0)  do  not  include  the  great  inequality  of  Jupiter. 

It  was  found,  however,  that  in  order  to  form  the  complete  arguments  of  the  inequalities  of  the  satellites,  as 
DE  DAMOISEAU  appears  to  have  done,  it  is  necessary  to  add  the  great  inequality.  So  that  in  the  formulae  for  the 
arguments  alone,  given  on  pages  (iv),  (v),  (vn),  (ix)  of  the  Introduction  to  the  Tables  Ecliptiques,  it  is  necessary 
to  write  J-(-  *>  instead  of  <t> . 

THE  FORMATION  OF  TABLE  III. 
The  Terms  in  (  J  -f-  <t>  -\-  3  E ). —  In  continuing  Table  III  of  each  satellite,  the  values  of  J,  <*,  </>!,  dr,  <5  E,  were 


computed  from  BOUVARD'S  Tables  at  half-year  intervals,  fa  being  equal  to  <!'\ 


The  results  of  this  compu- 


tation are  presented  in  the  following  table.     J  and  S  E,  columns  the  second  and  fifth,  are  expressed  in  centesimal 
arc.     J  +  <i>  ,  column  tho  third,  is  expressed  in  sexagesimal  arc. 

Ik  =  22'  11".5  (of  centesimal  arc), 
=  0°.  19903    (of  sexagesimal  arc). 

rA-1=  0.00730 


Year  and  tenth. 

J 

J-H 

*.  +  *• 

(!E 

1880.0  B 

+  29  56.6 

+  0?12934 

—  0.00165 

-0  63"7 

1880.5  B 

29  49.2 

0.14189 

—  0.00318 

—  0  19.1 

1881.0 

29  41.7 

0.16411 

—  0.00432 

+  0  28.3 

1881.5 

29  34.3 

0.19297 

—  0.00497 

0  72.9 

1882.0 

+  29  26.7 

-f  0.22440 

—  0.00499 

+  1  11.6 

*  Tables  Astronomifjiies  publi6es  par  le  Bureau  des  Longitudes  de  France,  contenant  les  Tables  de  Jupiter,  de  Saturue  et  d'Uranus, 
construites  d'apr&s  la  Th6orie  de  la  M6canique  Celeste,  par  M.  A.  BOUVARD,  Paris,  1821. 


10 


INTRODUCTION. 


Year  mid  ti-ntli. 

J 

J  +  <<> 

*  +  dr 

STt 

1882.0 

+  29  26.7 

+  0?22440 

—  0.00499 

+  i  li'.c 

1882  5 

29  19.2 

0.25309 

-  0.00454 

1  40.3 

1883.0 

29  11.6 

0.27666 

—  0.00363 

1  579 

1883.5 

29   3.9 

0.29263 

—  0.00248 

1  63.5 

1884.0  B 

28  96.3 

0.30115 

—  0.00120 

1  57.5 

1884.5  B 

28  88.6 

0.30277 

+  0.00003 

1  41.5 

1885.0 

+  28  80.9 

+  0.29894 

+  0.00115 

+  1  16.0 

1885.5 

28  73.2 

0.29088 

0.00207 

0  85.7 

1886.0 

28  65.3 

0.27967 

0.00275 

0  49.4 

1886.5 

28  57.5 

0.26640 

0.00322 

+  0  108 

1887.0 

28  49.6 

0.25174 

0.00343 

—  0  29.3 

1887.5 

+  28  41.8 

+  0.23672 

+  0.00331 

—  0  67.8 

1888  0  B 

28  33.9 

0.22196 

0.00295      —  1   4.0 

1888.5  B 

28  25.9 

0.20897 

000230      —  1  348 

1889.0 

28  17.9 

0.19846 

0.00142      —  1  58.6 

1889.5 

28   9.8 

0.19210 

+  0.00044 

—  1  72.6 

1890.0 

+  28   1.8 

+  0.19063 

—  0.00068 

—  1  75.5 

1890.5 

27  93.7 

0.19467 

-  0.00173      —  1  65.6 

1891.0 

27  85.6 

0.20436 

-  0.00270      —  1  42.0 

1891.5 

27  77.4 

0.21906 

—  0.00337      —  1   5.9 

1892.0  B 

27  69.2 

0.23743 

—  0.00377      —  0  59.5 

1892.5  B 

+  27  61.0 

+  0.25788 

—  0.00378      —  0   6.9 

1893.0 

27  52.7 

0.27843 

-  0.00348      +0  47.1 

1893.5 

27  44.4 

0.29665 

—  0.00292        0  96.9 

1894.0 

27  36.1 

0.31058 

—  0.00210        1  38.1 

1894.5 

27  27.7 

0.31931 

—  0.00122 

1  67.5 

1895.0 

+  27  19.3 

+  0.32211 

—  0.00026 

+  1  83.5 

1895.5 

27  10.9 

0.31916 

+  0.00063         1  86.0 

1896.0  B 

27   2.4 

0.31155 

0.00143 

1  75.8 

1896.5  B 

26  93.9 

0.30063 

000203 

1  54.4 

1897.0 

26  85.4 

0.28779 

0.00256 

1  23.9 

1897.5 

+  26  76.8 

+  0.27445 

+  0.00285 

+  0  86.5 

1898.0 

26  68.2 

0.26148 

0.00296      +  0  43.7 

1898.5 

26  59.6 

0.24971 

0.00282      —  0   0.4 

1899.0 

26  50.9 

0.23996 

0.00247      —  0  45.6 

1899.5 

26  42.2 

0.23291 

0.00185      —  0  89.0 

1900.0 

+  26  33.5 

+  0.22939 

+  0.00107 

—  1  28.3 

The  mean  synodic  revolutions  of  the  satellites  are 

I  =   1.769860478875 
II  =  3.554094157794 

III  =  7.166387201355 

IV  =16.753552411222, 

which  are  fifteen  times  the  factors  for  (  J  -j-  <t>  -\-  3  E  ).     The  data  already  presented  suffice  for  the  computation 
of  Table  III  of  the  first  satellite. 

The  Terms  in  ( 5  (7  —  2  «„).—  These  terms  of  Table  III,  satellites  II,  III,  IV,  are  functions  of  the  longitudes 
of  Jupiter  and  Saturn. 

1880.0         (  5  u  —  2  «.„  —  34°.542  )  =  84°.068 
Daily  motion  of  the  angle  (5w  —  2«0)  =  0°.00 1039596 

During  the  period   1880—1900  this  angle  plus  the  constant  is  so  near  90°  that  its  sine  varies  very  slowly,  and 
it  will  be  sufficient  to  compute  the  terms  involving  its  sine  for  every  fifth  year. 


INTRODUCTION. 


11 


II.  III. 

+(*)0».952sin(5«— 2«0— 34°.o42)      +(*)2'.823«iii(5ti— 2«0— 34°.542) 


1880.0 
1885.0 
1890.0 
1895.0 
1900.0 


+  0.95 
+  0.95 
-j-0.95 
-f  0.95 
+  0.95 


+  2.81 
+  2.82 
+  2.82 
+  2.82 
+  2.82 


III. 

+  is"  50 
+  15.54 
+  15.57 
+  15.58 
+  15.57 


The  Terms  in  (  II  — An  ),  (  II  — A,,, ),  etc. —  These  terms  of  Table  III,  satellites  II,  III,  IV,  are  functions  of  the 
longitude  of  the  ascending  node  of  the  equator  of  Jupiter  on  its  orbit,  and  of  the  longitudes  of  the  ascending  nodes 
of  the  orbits  of  these  satellites  on  their  fixed  planes. 

1880.0  (  ii-A,,  )  =  34K499 

1880.0  (  n- A,,,)  =  111.875 

1880.0  (n-A,v)  =  124.964 

Daily  motion  of  the  angle  (n  —  A,,  )  =  0°03306928964 
Daily  motion  of  the  angle  (  H— Am)  =  0.00699245908 
Daily  motion  of  the  angle  (H_AIV)  =  0.00189341824 

The  angle  (n  —  AJV  )  changes  so  slowly  that  the  computation  of  the  term  involving  ils  sine  for  every  fifth 
year  will  suffice.  The  term  in  (  n  —  Am)  nas  been  computed  partly  at  intervals  of  one,  and  partly  at  intervals  of 
two  years.  The  term  depending  on  (n  —  AH)  has  been  computed  at  half-year  intervals. 


„. 

III. 

IV. 

Year  and  tenth. 

—  (  ')'.K731-sin(  II  —  An  ) 

—  (*)5'.775sin(II  —  Am) 

+  l(i".(i!)4  siii  (  11  —  Aiv) 

B              Dill1. 

B                Dill1. 

8               Dift'. 

1880.0  B 

+     3.09      ,,,, 

—     5.36 

+     13.68 

1880.5  B 

2.10    ,02 

10 

1881.0 

1.08    ,02 

—     5.26 

1881.5 

+     0.06    ,02 

11 

1882.0 

0.96    ]fll 

—     5.15 

1882.5 

-     1-97    JOG 

13 

GO 

1883.0 

-     2.97     95 

—     5.02 

1883.5 

—     3.92      92 

13 

1884.0  B 

-     4.84      8C 

—     4.89 

1884.5  B 

-     5'70      80 

1885.0 

6.50      73 

89 

+     13.08 

1885.5 

—     7.23      f)4 

1886.0 

7.87         r,,; 

4.60 

1S86.5 

8.43        I,,; 

1887.0 

-     8'89      37 

33 

1887.5 

9.26      w 

65 

1888.0  B 

9.52      JB 

4.27 

1888.5  B 

-     9.68       5 

1889.0 

—     9.73       G 

37 

1889.5 

—     9.67      ](J 

1890.0 

—     9.51      07 

—     3.90 

+     12.  13 

1890.5 

-     9.24     38 

1891.0 

8.86      47 

30 

. 

1891.5 

•        H.39          r(; 

1892.0  B 

—     7.83      ('ir, 

3.51 

70 

(*)  This  inequality  is  not  givi'ii  by  the  theory  of  Laplace. 


12 


INTRODUCTION. 


Year  and  tenth. 

II. 

III. 

IV. 

—  (*)98.731  sin  (  n  —  An  ) 

—  (*  )  58.775  sin  (  n  —  Am  ) 

+  16".694  sin  (  n  —  Aiv  ) 

H           Biff. 

s                Biff. 

a               Biff. 

1892.0  B 

'  —     T^83      05 

—     3.51 

1892.5  B 

-     7.18     74 

70 

1893.0 

—     6.44     80 

42 

1893.5 

—     5.64     87 

1894.0 

-    4.77     91 

—     3.09 

1894.5 

—     3.86     gfi 

1895.0 

-     2.90    10d 

44 

+     11.73 

18955 

-     1-90    101 

1896.0  B 

-     0.89    103 

—     2.65 

1896.5  B 

+     0.14    ma 

1897.0 

L16     101 

47 

1897.5 

+     2.17     oo 

73 

1898.0 

3.16     (J5 

2.18 

1898.5 

4.H      90 

•      1899.0 

5.01      85 

4!) 

1899.5 

5.86     70 

1900.0 

+     6.65 

1.69 

-f     1100 

My  values  of  the  "perturbations  of  Jupiter  and  other  inequalities,"  Table  III,  for  the  epoch  1880.0,  do  not 
agree  precisely  with  those  given  by  DE  DAMOISEAU. 

For  farther  comparison  with  his  tables,  I  have  computed,  in  this  way,  Table  III  of  each  satellite  complete 
for  the  years  1878  and  1879 ;  and  while  the  method  is  probably  the  one  employed  by  DE  DAMOISEAU,  it  does  not 
suffice  to  reproduce  exactly  his  values  of  the  perturbations  (Table  III)  for  these  years. 

The  corrections  necessary  to  reduce  his  values  to  such  as  have  been  computed  in  the  manner  indicated  are  as 
follow : 


Satellite 


1878.0 
1879.0 
1880.0 


I. 

8 

+     I-7 
2.1 

+     2.1 


II. 

+     2.5 

3.1 

+     3.5 


III. 


+ 


7.2 
9.2 
8.6 


IV. 

+     16*2 

20.7 

+     19.5 


The  discrepancy  is  traceable  to  the  term 

(J  +  P+.SE), 

and  (JE  appears  to  have  been  reduced  by  DE  DAMOISEAU  from  the  epoch  1744.0;  while  the  epoch  of  S  E  of 
BOUVARD'S  Tables  is  1800.0. 

The  differences  alluded  to  are  less  than  the  accidental  errors  of  observation,  and  may  be  disregarded. 

For^precepts  for  the  use  of  the  tables  of  the  eclipses,  the  computer  is  referred  lo  the  Introduction  to  the 
Tab/t's  Ediptiques,  pages  (x) — (xvn). 

Table  A  has  been  adapted  from  advance  sheets  of  the  American  Ephemcrix  and  Nautical  Almanac,  for  1880, 
and  gives  the  longitudes  of  Observatories,  Paris  being  the  prime  meridian.  West  longitudes  are  considered  posi- 
tive. To  reduce  the  tabular  instant  of  an  eclipse  to  the  mean  solar  astronomic  time  of  any  meridian  having  a 
longitude  A  from  Paris,  it  is  necessary  to  apply  the  correction 

-(*  +  12"). 

THE  TABLES  OF  THE  CONFIGURATIONS.— Of  the  Tables  for  computing  the  configurations,  Table  I  of  each 
satellite  alone  requires  extension. 


(*)  This  inequality  is  not  given  by  tin-  tiimry  of  Lupluce. 


INTRODUCTION.  13 

The  data  for  the  continuation  of  the  column  "Mean  longitude,"  are  given  by  DE  DAMOISEAU,  Introduction, 
page  (in  ).  Whence  there  is  derived  the 

Motion  of  «!  in  365  days,  113.48258 
Motion  of  vl  in  366  days,  316.97157 
Motion  of  MH  in  365  days,  281.78815 
Motion  of  «,,  in  366  days,  23.16291 
Motion  of  um  in  365  days,  5.94095 
Motion  of  «I;I  in  366  days,  56.25860 
Motion  of  wlv  in  365  days,  313.45494 
Motion  of  wlv  in  366  days,  335.02605. 

There  was  adopted,  for  the  epoch  1880,  January  1,  Paris  mean  midnight, 

w,    =:    6  9?80 

ttn   =    4  3.87 

«,„  =    6  0.92 

«IV  =  11  17.40 

DE  DAMOISEAU  gives  no  explanation  of  the  method  of  formation  of  the  arguments  of  these  tables.  I  have, 
therefore,  continued  them  by  induction. 

For  precepts  for  the  use  of  the  tables  of  the  configurations,  the  computer  is  referred  to  the  Tables  Ecliptiques, 
pages  (193)— (199). 

ERRORS  IN  DE  DAMOISEAU'S  Tables  JScliptiques,  etc. —  Through  the  courtesy  of  Mr.  J.  R.  HIND,  F.  R.  S., 
the  Superintendent  of  the  British  Nautical  Almanac,  and  of  Professor  E.  O.  KENDALL,  of  the  University  of 
Pennsylvania,  I  have  been  enabled  to  make  the  appended  list  of  errors  and  corrections  more  complete  than 
it  would  otherwise  have  been. 


TABLES 


THE    FIKST 


TABLE  I. 


Epochs  of  the  Mean  Conjunctions 


YEARS. 

MEAN  CONJUNCTIONS. 

1 

2 

3 

4 

l);iys  and  parts  of  a  day, 
Paris  mean  civil  time. 

Fraction  of 
year. 

1880  B 

Jan.        li     in      - 
1        18     8   15.0 

0.002 

s.       0 
1  1     8.759 

"•          0 

11  29.91 

9  12?32 

4  24?05 

1881 

2         2  48  15.7 

0.003 

%  0    9.197 

0    0.99 

8  12.94 

3  24.76 

1882 

1       16  59  40.4 

0.002 

1    9.488 

0    0.34 

7  11.93 

8  24.74 

1883 

1        7  11    5.2 

0.001 

2    9.779 

11  29.68 

6  10.92 

1  24.72 

1884  B 

2       15  51     5.8 

0.004 

3  10.217 

0     0.76 

5   11.55 

0  25.42 

1885 

1        6    2  30.6 

0.001 

4  10.508 

0    0.10 

4   10.60 

5  25.38 

1886 

2      14  42  31.3 

0.004 

5  10.946 

0     1.19 

3  11.27 

4  26.05 

1887 

2        4  53  56.0 

0.003 

6  11.237 

0    0.53                 2  10.34 

9  25.99 

1888  B 

1      19    5  20.8 

0.002 

7  11.528 

11  29.87 

1     9.42 

2  25.93 

1889 

2        3  45  21.5 

0.003 

8  11.966 

0    0.96 

0  10.10 

1  20.61 

1890 

1       17  56  46.2 

0.002 

9  12.257 

0    0.30 

11     9.15 

6  26.56 

1891 

1        8    8  11.0 

0.001 

10  12.548              11  29.64 

10    8.19 

11  26.52 

1892  B 

2      16  48  11.7 

0.005 

11   12.986 

0    0.72 

9    8.80              10  27.2-2 

1893 

1        6  59  36.4 

0.001 

0  13.277 

0    0.07 

8    7.81 

3  27.20 

1894 

2      15  39  37.1 

0.004 

1   13.715                0    1.15 

7    8.43 

2  27.90 

1895 

2        5  51     1.8 

0.003 

2  14.006 

0     0.49 

6    7.47 

7  27.86 

1896  B 

1      20    2  26.6 

0.002 

3  14.297 

11  29.83 

5    6.53 

0  27.81 

1897 

2        4  42  27.3 

0.003 

4  14.735 

0    0.92 

4     7.20 

11  28.48 

1898 

1       18  53  52.0 

0.002 

5  15.026 

0    0.26 

3    6.28 

4  28.43 

1899 

1         9    5  16.8 

0.001 

6  15.316 

11  29.60 

2    5.35 

9  28.37 

1900 

2       17  45  17.5 

0.005 

7  15.754 

0    0.69                1    6.00                8  29.05 

SATELLITE. 


17 


and  the  Arguments  of  the  Inequalities. 


YEARS. 

5 

6 

1 

8 

9 

I 

II 

III 

1880  B 

*•    0 

4  C.I 

B.   0 

1  20.3 

»•    0 

2  12.0 

*•    0 

7  28.0 

"•    0 

7  5.0 

p-    0 

1  0.35 

*•   0 

0  11.9 

•B-    0 

4  22.2 

1881 

2  22.2 

2  18.2 

3  12.3 

5  1.0 

4  7.2 

2  0.82 

1  24.5 

5  25.3 

1882 

4  7.2 

3  10.0 

4  12.0 

2  3.8 

1  7.5 

3  1.18 

3  0.9 

0  28.2 

1883 

5  22.1 

4  13.7 

5  11.0 

1  1  0.0 

10  7.8 

4  1.52 

4  19.3 

8  1.1 

1884  B 

4  8.2 

5  11.0 

0  11.4 

8  9.0 

7  9.5 

5  1.99 

0  1.9 

9  4.1 

1885 

5  23.1 

0  9.2 

7  11.0 

5  11.8 

4  9.8 

0  2.28 

7  14.2 

10  6.9 

1880 

4  9.1 

7  7.1 

8  10.7 

2  15.3 

1  11.4 

7  2.70 

8  20.8 

11  9.9 

1887 

5  24.0 

8  4.7 

9  10.3 

11  17.5 

10  11.7 

8  2.97 

10  9.1 

0  12.7 

1888  B 

7  8.9 

9  2.4 

10  9.9 

8  19.7 

7  12.0 

9  3.24 

11  21.4 

1  15.0 

1889 

5  25.0 

10  0.2 

11  9.0 

5  23.3 

4  13.7 

10  3.05 

1  4.0 

2  18.5 

1890 

7  9.9 

10  27.9 

0  9.2 

2  25.5 

1  14.0 

11  3.94 

2  1G.3 

3  21.4 

1891 

8  24.8 

11  25.0 

I  8.8 

11  27.7 

10  14.3 

0  4.25 

3  28.7 

4  24.2 

1892  B 

7  10.9 

0  23.5 

2  8.0 

9  1.3 

7  15.9 

1  4.72 

5  11.2 

5  27.3 

1893 

8  25.8 

1  21.2 

3  8.2 

0  3.5 

4  16.2 

2  5.0G 

0  23.0 

7  0.1 

1894 

7  11.9 

2  19.1 

4  8.0 

3  7.0 

1  17.8 

3  5.53 

8  0.2 

8  3.2 

1895 

8  20.8 

3  10.8 

5  7.0 

0  9.2 

10  18.2 

4  5.84 

9  18.0 

9  C.O 

1890  B 

10  11.8 

4  14.5 

0  7.2 

9  11.4 

7  18.5 

5  0.12 

1  1  0.9 

10  8.9 

1897 

8  27.8 

5  12.3 

7  0.9 

0  15.0 

4  20.1 

0  0.54 

0  13.5 

11  11.8 

1898 

10  12.7 

0  9.9 

8  0.5 

3  17.2 

1  20.1 

7  0.81 

1  25.8 

0  14.7 

1899 

11  27.0 

7  7.0 

9  C.O 

0  19.4 

10  20.7 

8  7.08 

3  8.1 

1  17.5 

1900 

10  13.0 

8  5.4 

10  5.8 

9  23.0 

7  22.4 

9  7.51 

4  20.7 

2  20.5 

18 


THE    FIRST    SATELLITE. 


TABLE  III.          Perturbations  of  Jupiter  and  other  Inequalities, 


0.1179907  (J 


E)  +  493.2  (0,  +  Jr). 


Year?  and 
tenths. 

Perturb. 

Diff. 

Years  and 

tenths. 

Perturb. 

Diff. 

Years  and 
tenths. 

Perturb. 

Diff. 

Years  and 
lenths. 

Perturb. 

Diff. 

m     s 

in      s 

Ill        S 

m     s 

1880.0 

0  51.7 

s 

1883.0 

2     1.7 

s 

1886.0 

2    2.1 

s 

1889.0 

1   19.0 

s 

+0.8 

+1.9 

-1.3 

-1.0 

1 

0  52.5 

1 

2    3.6 

1 

2    0.8 

1 

1  18.0 

1.1 

1.6 

-1.4 

-0.8 

2 

0  53.6 

2 

2    5.2 

2 

1  59.4 

2 

1   17.2 

1.3 

1.6 

-1.4 

-0.8 

3 

0  54.9 

3 

2    0.8 

3 

1  58.0 

3 

1   16.4 

1.4 

1.4 

-1.4 

-0.6 

4 

0  56.3 

4 

2    8.2 

4 

1  56.6 

4 

1  15.8 

+1.7 

+1.2 

-1.5 

-0.6 

5 

0  58.0 

5 

2    9.4 

5 

1  55.1 

5 

1   15.2 

1.1 

-1.5 

-0.5 

0 

0  59.8 

1.8 

6 

2  10.5 

6 

1  53.0 

0 

1   14.7 

o  n 

0.9 

-1.5 

-0.3 

7 

1     1.8 

IM) 

7 

2  11.4 

7 

1  52.1 

7 

1   14.4 

0.8 

-1.5 

-rO.3 

8 

1     3.9 

••1 

8 

2  12.2 

8 

1  50.0 

8 

1  14.1 

0.6 

-0.2 

9 

1     0.2 

!£.J 

9 

2  12.8 

9 

1  49.1 

9 

1  13.9 

,     +2.5 

+0.5 

-1.6 

0.0 

1881.0 

8.7 

1884.0 

2  13.3 

1887.0 

1  47.5 

1890.0 

1  13.9 

0.4 

—1.6 

+0.1 

1 

11.9 

<i.o 

1 

2  13.7 

1 

1  45.9 

j 

1  14.0 

0.3 

—1.6 

0.2 

2 

13.9 

y.v 

2 

2  14.0 

2 

1  44.3 

2 

1   14.2 

+0.1 

—1.6 

0.3 

3 

16.6 

y.  / 

3 

2  14.1 

3 

1  42.7 

3 

1  14.5 

o  o 

0.0 

-1.6 

0.5 

4 

19.5 

y.y 

4 

2  14.1 

4 

1  41.1 

4 

1   15.0 

+2.9 

-0.1 

-1.6 

+0.5 

5 

1  2.U 

5 

2  14.0 

5 

1  39.5 

5 

1  15.5 

3.0 

-0.2 

—1.6 

0.7 

6 

1  25.4 

2.9 

6 

2  13.8 

-0.3 

6 

1  37.9 

—1.5 

6 

1  16.2 

0.8 

7 

1  28.3 

7 

2  13.5 

7 

1  36.4 

7 

1   17.0 

3.1 

-0.4 

-1.6 

0.9 

8 

1  31.4 

8 

2  13.1 

8 

1  34.8 

8 

1  17.9 

2.8 

—0.5 

—1.5 

1.0 

9 

1  34.2 

9 

2  12.6 

9 

1  33.3 

9 

1   18.9 

+2.9 

-0.6 

-1.5 

+  1.1 

188-2.0 

1  37.1 

2.8 

1885.0 

2  12.0 

-0.7 

1888.0 

1  31.8 

-1.5 

1891.0 

1  20.0 

1.3 

1 

1  39.9 

1 

2  11.3 

1 

1  30.3 

1 

1  21.3 

2.9 

-0.8 

—1.5 

1.4 

2 

1  42.8 

2 

2  10.5 

2 

1  28.8 

2 

1  22.7 

2.7 

—0.8 

—1.4 

1.5 

3 

1  45.5 

3 

2    9.7 

3 

1  27.4 

3 

1  24.2 

-0.9 

—1.4 

1.5 

4 

1  48.2 

4 

2    8.8 

4 

1  26.0 

4 

1  25.7 

+2.5 

-1.0 

-1.3 

+1.6 

5 

1  50.7 

5 

2    7.8 

5 

1  24.7 

5 

1  27.3 

2.5 

-1.0 

-1.3 

1.8 

6 

1  53.2 

6 

2    6.8 

6 

1  23.4 

6 

1  29.1 

2.3 

—I.I 

—1.2 

1.8 

7 

1  55.5 

2.2 

7 

2    5.7 

-1.2 

7 

1  22.2 

-1.1 

7 

1  30.9 

1.9 

8 

1  57.7 

8 

2    4.5 

8 

1  21.1 

8 

1  32.8 

2.1 

—1.2 

-1.1 

1.9 

9 

1  59.8 

9 

2    3.3 

9 

1  20.0 

9 

1  34.7 

+1.9 

-1.2 

-1.0 

+2.0 

1883.0 

2    1.7 

1886.0 

2    2.1 

1889.0 

1  19.0 

1892.0 

1  36.7 

THE    FIRST    SATELLITE. 


19 


TABLE  III.  Perturbations  of  Jupiter  and  other  Inequalities. 


0.1 179907  (J  +  0  -f-  eJ  E)  +  493.2  (^  +  S  r). 


Years  and 
tenths. 

Perturb. 

Diff. 

Will's  :mil 
tenths. 

IVrtiu-li. 

Diff. 

Yearn  :ui<l 
tenths. 

Perturb. 

Diff. 

Years  and 
tentlis. 

Perturb. 

Diff. 

in     s 

Ill        S 

Ill        S 

in     s 

1893.0 

1  30.7 

s 
+3.1 

1894.0 

2  JO.I 

s 

+1.3 

1890.0 

2-19.8 

s 
-0.9 

1898.0 

1  54.2 

s 
-1.4 

1 

1  38.8 

a.i 

1 

2  17.4 

i  .a 

1 

2  18.9 

-1.0 

1 

1  52.8 

-1.4 

2 

1  40.9 

S.9 

2 

2  18.0 

j.i 

2 

2  17.9 

-1.0 

2 

1  51.4 

-1.3 

a 

1  43.1 

S.I 

3 

2  19.7 

0.9 

3 

2  10.9 

-1.1 

3 

1  50.1 

-1.4 

4 

1  45.2 

4 

2  20.0 

4 

2  15.8 

4 

1  48.7 

+2.2 

+0.8 

-1.2 

-1.3 

5 

1  47.4 

2.2 

5 

2  21.4 

0.7 

5 

2  14.6 

-1.2 

5 

I  47.4 

-1.2 

C 

1  49.C 

2.2 

0 

2  2-2.1 

0.6 

0 

2  13.4 

-1.3 

0 

1  40.2 

-1.3 

7 

1  51.8 

S.3 

7 

2  22.7 

0.5 

7 

2  12.2 

-1.3 

7 

1  44.9 

-1.3 

8 

1  54.0 

2.2 

8 

2  23.2 

o.:) 

8 

2  10.9 

-1.3 

8 

1  43.7 

-1.2 

9 

1  50.2 

.       9 

2  23.5 

9 

2    9.0 

9 

1  42.5 

+2.1 

+0.2 

-1.3 

-1.1 

1893.0 

1  58.3 

2.1 

1895.0 

2  23.7 

+0.1 

1897.0 

2    8.3 

-1.4 

1899.0 

1  41.4 

-1.1 

1 

2    0.4 

a.i 

1 

2  23.8 

0.0 

1 

2    0.9 

-1.4 

1 

1  40.3 

-1.0 

2 

2    2.5 

a.o 

2 

2  23.8 

-0.2 

2 

2    5.5 

-1.4 

2 

1  39.3 

-1.0 

3 

2    4.5 

1.9 

3 

2  23.0 

-0.3 

3 

2    4.1 

-1.4 

3 

1  38.3 

-1.0 

4 

2    6.4 

4 

2  23.3 

4 

2    2.7 

4 

1  37.3 

+1.8 

-0.3 

-1.4 

-0.9 

5 

2    8.2 

1.8 

5 

2  23.0 

-0.5 

5 

2    1.3 

-1.4 

5 

1  30.4 

-0.8 

6 

2  10.0 

1.7 

6 

2  22.5 

-0.5 

0 

1  59.9 

-1.4 

0 

1  35.0 

-0.7 

7 

2  11.7 

1.6 

7 

2  22.0 

-0.7 

7 

1  58.5 

-1.5 

7 

1  34.9 

-0.7 

8 

2  133 

1.5 

8 

2  21.3 

-0.7 

8 

1  57.0 

-1.4 

8 

1  34.2 

-0.6 

9 

2  14.8 

9 

2  20.0 

9 

1  55.0 

9 

1  33.0 

+1.3 

-0.8. 

-1.4 

-0.5 

1894.0 

2  1C.1 

1896.0 

2  19.8 

1898.0 

1  54.2 

1900.0 

1  33.1 

20 


THE    SECOND 


TABLE  I. 


Epochs  of  the  Mean  Conjunctions 


YEAUS. 

MEAN  COXJUNCTIONS. 

1 

2 

3 

4 

Dave  and  parts  of  a  day, 
Paris  mean  civil  time. 

Fraction  of 
year. 

1880  B 

Jan.      h    m    s 
3        4    1    1,0 

0.006 

^-        0 

11     8.879 

B.        o 

0    1.34 

B.        o 

9  13.63 

s.      0 
1  24.63 

1881 

3        5  44  15,7 

0,006 

0    9.293 

0    2.14 

8  13.98 

0  25.21 

1882 

4        7  27  30,5 

0.009 

1    9.707 

0    2.94 

7  14.31 

11  25.81 

1883 

1      19  52  51,5 

0.002 

2    9.826 

0    0.23 

6  11.43 

4  24.94 

1884  B 

2      21  36    6.2 

0.005 

3  10.240 

0    1.03 

5  11.80 

3  25.52 

1885 

2      23  19  20.9 

0.005 

4  10.654 

0    1.83 

4  12.18 

2  26.08 

1886 

4        1    2  35,6 

0.008 

5  11.068 

0    2.64 

3  12.59 

1  20.64 

1887 

1       13  27  56,6 

0.001 

6  11.187 

11  29.93 

2    9.80 

6  25.72 

1888  B 

2      15  11  11.4 

0.004 

7  11.601 

0    0.73 

1  10.21 

5  20.27 

1889 

2      16  54  26.1 

0.005 

8  12.015 

0    1.53 

0  10.02 

4  20.83 

1890 

3      18  37  40.8 

0.008 

9  J  2.429 

0    2.33 

11  11.02 

3  27.39 

1891 

1        7    3    1.8 

0.001 

10  12.548 

11  29.63 

10    8.18 

8  20.50 

1892  B 

2        8  46  16.6 

0.004 

11  12.961 

0    0.43 

9    8.53 

7  27.08 

1893 

2      10  29  31.3 

0.004 

0  13.375 

0    1.23 

8    8.88 

6  27.67 

1894 

3      12  12  46.0 

0.007 

1  13.789 

0    2.03 

7    9.23 

5  28.25 

1895 

4      13  56    0.7 

0.010 

2  14.203 

0    2.83 

6    9.61 

4  28.82 

1896  B 

2        2  21  21.7 

0.003 

3  14.322 

0    0.13 

5    0.80 

9  27.92 

1897 

2        44  36.5 

0.003 

4  14.736 

0    0.93 

4    7.21 

8  28.47 

1898 

3        5  47  51.2 

0.006 

5  15.150 

0    1.73 

3    7.62 

7  29.02 

1899 

4        7  31    5.9 

0.009 

6  15.503 

0    2.53 

2    8.03 

6  29.58 

1900 

1      19  56  26.9 

0.002 

7  15.682 

11  29.83 

1     5.22     . 

11  28.67 

SATELLITE. 


-21 


and  the  Arguments  of  the  Inequalities. 


VK.VUS. 

5 

6 

7 

8 

I 

II 

• 

III 

IV 

1880  B 

R.    o 

1  20.2 

«.    0 

2  12.7 

s-    0 

7  29.1 

s.   0 
7  G.G 

S.   o 

1  0.46 

s.   0 
0  12.05 

S.    o 

4  22.4 

*•   o 
5  5.4 

1881 

2  18.) 

3  12.4 

5  2.4 

4  8.1 

2  0.92 

1  24.01 

5  25.4 

0  G.G 

1882 

3  15.9 

4  12.2 

2  5.8 

1  9.5 

3  1.39 

3  7.19 

0  28.4 

7  7.8 

1883 

4  13.5 

5  11.7 

11  G.4 

10  8.2 

4  1.57 

4  19.35 

8  1.1 

8  8.0 

1884  B 

5  11.3 

G  11.4 

8  9.8 

7  9.7 

5  2.01 

G  1.90 

9  4.1 

9  9.7 

1885 

C  9.2 

7  11.2 

5  13.1 

4  11.  1 

G  2.42 

7  14.42 

10  7.1 

10  10.8 

188G 

7  C.9 

8  10.8 

2  1C.4 

1  12.5 

7  2.82 

8  2G.93 

11  10.0 

11  11.9 

1887 

8  4.4 

9  10.2 

11  17.1 

10  11.3 

8  2.92 

10  9.01 

0  12.7 

0  12.7 

1888  B 

9  2.2 

10  9.9 

8  20.4 

7  12.7 

9  3.30 

11  21.50 

1  15.0 

1  13.8 

1889 

10  0.0 

11  9.C 

5  23.7 

4  14.1 

10  3.70 

1  4.00 

2  18.0 

2  14.9 

1890 

10  27.8 

0  9.3 

2  27.0 

1  15.5 

11  4.11 

2  10.52 

3  21.  G 

3  10.0 

1891 

11  25.4 

1  8.8 

11  27.7 

10  14.3 

0  4.24 

3  28.G4 

4  24.2 

4  10.8 

1892  B 

0  23.2 

2  8.5 

9  1.0 

7  15.7 

1  4.09 

5  11.20 

5  27.2 

5  18.0 

1893 

1  21.0 

3  8.3 

G  4.4 

4  17.1 

2  5.15 

C  23.70 

7  0.2 

G  19.1 

1894 

2  18.9 

4  8.0 

3  7.7 

1  18.5 

3  5.CO 

8  G.32 

8  3.3 

7  20.2 

1895 

3  1(1.7 

5  7.8 

0  11.0 

10  19.9 

4  G.03 

9  18.85 

9  G.2 

8  21.4 

189C  B 

4  14.2 

G  7.2 

9  11.7 

7  18.7 

5  G.14 

11  0.95 

10  8.9 

9  22.2 

1897 

5  12.0 

7  G.9 

G  15.0 

4  20.1 

G  G.54 

0  13.45 

11  11.8 

10  23.3 

1898 

0  9.8 

8  6.G 

3  18.3 

1  21.5 

7  G.93 

1  25.95 

0  14.8 

11  24.3 

1893 

7  7.0 

9  G.3 

0  21.  G 

10  22.9 

8  7.32 

3  8.45 

1  17.8 

0  25.4 

1900 

8  5.1 

10  5.7 

9  22.3 

7  21.7 

9  7.43 

4  20.55 

2  20.4 

1  20.2 

22 


THE    SECOND    SATELLITE. 


TABLE  III.          Perturbations  of  Jupiter  and  other  Inequalities. 


0,2369396  (  J  +  ^  +  <5E)  +  493.2  (ft  +  <?»•)  +  (*)  0.952  sin  (5u  —  2«0  — 34.542)  —  (*)  9.731  sin  ( II— A,,  ). 


Diff. 

Years  and 
tenths. 

Perturb. 

Diff. 

Years  and 
tenths. 

Perturb. 

Diff. 

Years  and 
U'Mtlis. 

Perturb. 

Piff. 

Years  and 
tenths. 

Perturb. 

m    s 

m    s 

in     s 

m    s 

1880.0 

1  48.7 

s 
+1.7 

1883.0 

4    4.3 

R 

+3.3 

1886.0 

3  56.8 

s 

-2.8 

1889.0 

2  29.1 

8 

-1.8 

1 

1  50.4 

1 

4    7.6 

1 

3  54.0 

1 

2  27.3 

2.0 

3.1 

—2.9 

—1.6 

2 

1  52.4 

2 

4  10.7 

2 

3  51.1 

2 

2  25.7 

2.5 

2.7 

-2.9 

—1.4 

3 

1  54.9 

3 

4  13.4 

3 

3  48.2 

3 

2  24.3 

2.9 

2.5 

-3.0 

-1.2 

4 

1  57.8 

4 

4  15.9 

4 

3  45.2 

4   |     2  23.1 

+3.3 

+2.2 

-3.1 

-1.0 

5 

2    1.1 

5 

4  18.1 

r 

3  42.1 

5   !     2  22.1 

3.6 

1.7 

—3.1 

—0.8 

6 

2    4.7 

6 

4  19.8 

G 

3  39.0 

(] 

2  21.3 

3.9 

1.8 

—3.1 

—0.6 

7 

2    8.6 

7 

4  21.4 

7 

3  35.9 

7 

2  20.7 

4.3 

1.3 

-3.2 

—0.4 

8 

2  12.8 

8 

4  22.7 

8 

3  32.7 

8 

2  20.3 

4.5 

1.0 

-3.2 

—0.2 

9 

2  17.3 

9 

4  23.7 

9 

3  29.5 

•0 

2  20.1 

+4.8 

+0.8 

-3.3 

+0.1 

1881.0 

2  22.1 

18810 

4  24.5 

1887.0 

3  26.2 

1890.0 

2  20.2 

5.0 

0.4 

-3.2 

0.3 

1 

2  27.1 

5.2 

1 

4  24.9 

+0.2 

1 

3  23.0 

-3.3 

1 

2  20.5 

0.6 

2 

2  32.3 

2 

4  25.1 

2 

3  19.7 

2 

2  21.1 

5.4 

0.0 

-3.3 

0.8 

3 

2  37.7 

3 

4  25.1 

3 

3  16.4 

3        2  21.9 

5.6 

-0.2 

-3.3 

1.0 

4 

2  43.3 

4 

4  24.9 

4 

3  13.1 

4        2  22.9 

+5.7 

-0.5 

-3.2 

+1.3 

5 

2  49.0 

5 

4  24.4 

5 

3    9.9 

5   !     2  24.2 

5.7 

-0.7 

-3.2 

1.6 

6 

2  54.7 

6 

4  23.7 

6 

3    6.7 

6 

2  25.8 

5.7 

-0.9 

-3.2 

1.7 

7 

3    0.4 

7 

4  22.8 

7 

3    3.5 

7 

2  27.5 

5.7 

-1.1 

-3.1 

2.0 

8 

3   'G.I 

8 

4  21.7 

8 

3    0.4 

8 

2  29.5 

5.7 

-1.3 

-3.1 

2.2 

9 

3  11.8 

9 

4  20.4 

9 

2  57.3 

9 

2  31.7 

+5.6 

-1.5 

-3.1 

+3.5 

1882.0 

3  17.4 

5.5 

1885.0 

4  18.9 

-1.6 

1888.0 

2  54  .2 

-2.9 

1891.0 

2  34.2 

2.7 

1 

3  22.9 

1 

4  17.3 

1 

2  51.3 

1 

2  36.9 

5.5 

-1.8 

-2.9 

2.9 

2 

3  28.4 

5.2 

2 

4  15.5 

-1.9 

2 

2  48.4 

-2.8 

2 

2  39.8 

3.1 

3 

3  33.0 

3 

4  33.6 

3 

2  45.6 

3 

2  42.9 

5.1 

-2.0 

-2.7 

3.3 

4 

3  38.7 

4 

4  11.6 

4 

2  42.9 

4 

2  46.2 

+4.8 

-2.2 

-2.7 

+3.4 

5 

3  43.5 

5 

4    9.4 

5 

2  40.2 

5 

2  49.6 

4.7 

-2.3 

-2.5 

3.7 

C 

3  48.2 

C 

4    7.1 

6 

2  37.7 

6 

2  53.3 

4.4 

-3.4 

-2.3 

3.8 

7 

3  52.0 

7 

4    4.7 

7 

2  35.4 

7 

2  57.1 

4.1 

-2.6 

-2.3 

3.9 

8 

3  56.7 

8 

4    2.1 

8 

2  33.1 

8 

3    1.0 

3.9 

-2.6 

-2.1 

4.0 

9 

4    0.6 

9 

3  59.5 

9 

2  31.0 

9 

3    5.0 

+3.7 

-2.7 

-1.9 

+4.2 

1883.0 

4    4.3 

1886.0 

3  56.8 

1889.0 

2  29.1 

1892.0 

3    9.2 

THE    SECOND    SATELLITE, 


23 


TABLE  III.          Perturbations  of  Jupiter  and  other  Inequalities, 


.1  +  9  +  6K )  +  4'J3.a  (<fi 


0  s 


Years  and 
tenths. 

Pert  ii  i-l>. 

Diff. 

Years  and 

tMltll.-. 

Perturb. 

Diff. 

Years  and 

tl'lltllS. 

Perturb. 

Diff. 

Yeare  and 
tenths. 

Perturb. 

Diff. 

Ill         S 

m     s 

in     s 

in     s 

1892.0 

3    9.2 

8 

+4.3 

1894.0 

4  30.6 

s 
+2.7 

1896.0 

4  40.0 

8 

-1.7 

1898.0 

3  52.0 

H 

-2.6 

] 

3  13.5 

4.4 

1 

4  33.3 

2.4 

1 

4  38.3 

-1.8 

1 

3  49.4 

-2.6 

2 

3  17.9 

4.4 

2 

4  35.7 

2.8 

2 

4  36.5 

-1.9 

2 

3  46.8 

-2.5 

3 

3  22.3 

4.5 

3 

4  37.9 

2.0 

3 

4  34.6 

-2.1 

3 

3  44.3 

-2.5 

4 

3  26.8 

4 

4  39.9 

4 

4  32.5 

4 

3  41.8 

+4.5 

+1.8 

-2.1 

-2.4 

5 

3  31.3 

4.5 

5 

4.41.7 

1.5 

5 

4  30.4 

-2.3 

5 

3  39.4 

-2.3 

6 

3  35.8 

4.» 

6 

4  43.2 

1.3 

6 

4  28.1 

-2.3 

<; 

3  37.  L 

-3.3 

7 

3  40.4 

4.5 

7 

4  44.5 

1.0 

7 

4  25.8 

-2.4 

7 

3  34.8 

-2.3 

8 

3  44.9 

4.5 

8 

4  45.5 

0.7 

8 

4  23.4 

-2.5 

8 

3  32.5 

-2.1 

g 

3  49.4 

9 

4  46.2 

9 

4  20.9 

9 

3  30.4 

+4.4 

+0.5 

-2.5 

-2.0 

1893.0 

3  53.8 

4.4 

1895.0 

4  46.7 

+0.3 

1897.0 

4  18.4 

-^.6 

1899.0 

3  28.4 

-2.0 

] 

3  58.2 

4.2 

1 

4  47.0 

+0.1 

1 

4  15.8 

-2.6 

1 

3  26.4 

-1.9 

2 

4    2.4 

4.1 

2 

4  47.1 

-0.2 

2 

4  13.2 

-2.6 

2 

3  24.5 

-1.8 

3 

4    6.5 

4.0 

3 

4  46.9 

-0.1 

3 

4  10.6 

-2.6 

3 

3  22.7 

-1.6 

4 

4  10.5 

4 

4  46.5 

4 

4    8.0 

4 

3  21.1 

+3.8 

-0.6 

-2.7 

-1.5 

5 

4  14.3 

3.6 

5 

4  45.9 

-0.9 

5 

4    5.3 

-2.7 

5 

3  19.0 

-1.5 

6 

4  17.9 

3.5 

6 

4  45.0 

-1.0 

6 

4    2.6 

-2.7 

6 

3  18.1 

-1.3 

7 

4  21.4 

3.3 

7 

4  44.0 

-1.2 

7 

3  50.9 

-2.6 

7 

3-16.8 

-1.1 

8 

4  24.7 

3.0 

8 

4  42.8 

-1.3 

8 

3  57.3 

-2.7 

8 

3  K.7 

-0.9 

9 

4  27.7 

9 

4  41.5 

9 

3  54.6 

9 

3  14.8 

+3.9 

-1.5 

-2.6 

-0.9 

1894.0 

4  30.6 

1896.0 

4  40.0 

1898.0 

3  52.0 

1900.0 

3  13.9 

+ 

24 


THE    THIRD 


TABLE  I. 


Epochs  of  the  Mean  Conjunctions 


YEARS. 

MEAN  CONJUNCTIONS. 

1 

2 

3 

4 

5 

Days  and  parts  of  a  day, 
I'arisinciiii  civil  time. 

Fraction  of 
year. 

1880  B 

Jan.       h    m      s 
4        6  13  11.0 

0.009 

S.         o 

1  1     8.974 

S.         o 

0    2.40 

8.         o 

9  14.  (iti 

"•         0 

3  20.2 

"•         0 

tl  17.0 

1881 

3      17  52  39.6    '      0.008 

0    9.339    !      0    2.08 

8  14.48 

1  20.8 

11  24.1 

1882 

4        5  32    8.2    :      0.009 

1    9.705          0    2.91 

7  14.28 

11  21.0 

2    0.0 

1883 

4      17  11  30.7 

0.010 

2  10.070 

0    3.13 

0  14.09 

9  22.2 

4     7.1 

1884  B 

5        4  51    5.3 

0.012 

3  10.l:r> 

0    3.35 

5  13.92 

7  22.9 

0  13.5 

1885 

4      16  30  33.9 

0.0  10 

4  10.801 

0    3.58 

4  13.78 

5  23.0 

8  20.0 

1886 

5        4  10    2.4 

0.011 

5  11.100 

0    3.80 

3  13.00 

3  24.2 

10  20.4 

1887 

5      15  49  31.0 

0.013 

0  11.531 

0    4.02 

2  13.54 

1  24.8 

1     2.8 

1888  B 

0        3  28  59.G 

0.014 

7  11.897 

0    4.24 

1  13.43 

11  25.4 

3    9.3 

1889 

5      15    8  28.1 

0.013 

8  12.202 

0    4.47 

0  13.31 

9  20.1 

5  15.7 

1890 

G        2  47  50.7 

0.014 

9  12.627 

0    4.69 

11  13.17 

7  20.7 

7  22.2 

J891 

6      14  27  25.3 

0.015 

10  12.993 

0    4.91 

10  13.02 

5  27.4 

9  28.6 

1892  B 

7        20  53.8 

0.010 

11  13.358 

0    5.14 

9  12.84 

3  28.0 

0    5.1 

1893 

6      13  40  22.4 

0.015 

0  13.723 

0    5.30 

8  12.00 

1  28.7 

2  11.0 

1894 

7        1  25  51.0 

0.010 

1  14.088 

0    5.58 

7  12.48 

11  29.4 

4  18.0 

1895 

7      13    5  19.5 

0.018 

2  14.454 

0    5.80 

0  12.33 

10    0.1 

0  24.5 

1890  B 

0      20  45  12.2 

0.000 

3  14.223 

11  28.90 

5    5.73 

7  24.8 

2    4.9 

1897 

7      12  24  16.6 

0.018 

4  15.184 

0    6.25 

4  12.08 

6     1.3 

11    7.4 

1898 

0      20    4    9.4 

0.000 

5  14.954 

11  29.41 

3    5.49 

3  20.1 

0  17.8 

1899 

1        7  43  37.9 

0.001 

6  15.319 

11  29.63 

2    5.37 

1  20.7 

8  24.2 

1900 

1      19  23    6.5 

0.002 

7  15.684 

11  29.86 

1    5.24 

11  27.3 

11     0.7 

SATELLITE. 


and  the  Arguments  of  the  Inequalities. 


-25 


UNIVERSITY 


YKAKS. 

G 

1 

8 

9 

1 

11 

111 

IV 

I860  B 

x-      o 
1  20.:{ 

»•         0 

•i  12.8 

8.          0 

8     0.0 

*•         0 

7     7.5 

s.    0 
1   0.45 

s.      0 
4  22.47 

5    & 

s.      0 
0  12.1 

1881 

2   18.1 

3  12.5 

5    2.9 

4     8.5 

2  0.85 

5  25.43 

6    0.0 

1  24.0 

1882 

X  15.D 

4   12.2 

2    5.7 

1     9.4 

3  1.28 

(5  28.41 

7     7.8 

3     7.1 

1883 

4   13.7 

5  11.9 

1  1    8.<; 

10  10.4 

4  1.70 

8     1.39 

8     8.9 

4  19.0 

1884  B 

5   11.5 

II   II.  (j 

8   11.5 

7  11.4 

.     5  2.09 

9    4.34 

9  10.0 

0    2.1 

1885 

0    9.3 

7   11.3 

5  14.4 

4  12.4 

6  2.4(5 

10    7.20 

10  11.0 

7  14.5 

1880 

7     7.0 

8  11.0 

2  17.3 

1    13.4 

7  2.81 

11   10.17 

11   12.0 

8  20.9 

1887 

8     4.8 

!)   10.15 

11  20.2 

10  14.3 

8  3.15 

0  13.06 

0  13.1 

10    9.4 

1888  B 

9     2.5 

10  10.2 

8  23.1 

7  15.3 

9  3.49 

1   15.90 

1   14.1 

11  21.8 

1883 

10    0.2 

11     9.9 

5  2(i.O 

4   1(5.3 

10  3.83 

2  18.86 

2  15.2 

1     4.2 

1890 

10  28.0 

0    9.5 

2  28.8 

1    17.3 

11  4.19 

3  21.78 

3   10.2 

2  10.7 

1891 

11  25.8 

1     9.2 

0     1.7 

10  18.2 

0  4.57 

4  24.71 

4  17.3 

3  29.1 

1892  li 

o  23.0 

2    8.9 

9    4.0 

7  19.2 

1  4.97 

5  27.07 

5  18.4 

5  11.0 

1893 

1  21.4 

3    8.0 

(i    7.5 

4  20.2 

2  5.38 

7     0.04 

0  19.5 

0  24.1 

181)4 

2  1!>.2 

4     8.3 

3  10.4 

1  21.2 

3  5.78 

8    3.59 

7  20.6 

8     0.0 

1895 

0  10.9 

5    8.0 

0  13.3 

10  22.2 

4  C.1G 

9    0.53 

8  21.0 

9  19.1 

IrtKi  15 

4  14.1 

0    7.1 

9  10.8 

7   17.8 

5  5.92 

10    8.80 

9  22.1 

11     0.7 

lew 

5  12.4 

7     7.3 

0  19.0 

4  24.1 

(i  6.8(5 

11   12.34 

10  23.7 

0  14.0 

1808 

0    9.0 

8    0.4 

3  1(5.0 

1   19.8 

7  (5.01 

0  14.60 

11  24.2 

1  25.5 

1899 
1900 

7     7.4 
8     5.1 

9    (i.O 
10     5.7 

0  19.5 
9  22.3 

10  20.8 
7  21.7 

8  0.90 
9  7.31 

1   17.50 
2  20.41 

0  25.2 
1  20.2 

3    8.0 
4  20.4 

THE    THIRD    SATELLITE. 


TABLE  III.  Perturbations  of  Jupiter  and  other  Inequalities. 


0.47/750  (J  +  f>  +  <5  F.  )  +  49;i.li  (0,  +  <?  r)  +  (*)  '<>.8y3  sin  (5  u  —  2  »/„  —  34.542)  —  (*)  5.77.')  sin  (II  —  A,,, ). 


Yeai-s  and 
tenths. 

Perturb. 

Ditf. 

Years  and 
tenths. 

Perturb. 

Diff. 

Years  and 
tenths. 

Perturb. 

Diff. 

Years  and 
tenths. 

Perturb. 

Diff. 

m     a 

m     s 

in     s 

m     s 

1880.0 

3  29.2 

s 

1883.0 

8   1G.2 

s 

188G.O 

8     8.3 

8 

1889.0 

5  16.3 

s 

+4.0 

+7.1 

-5.4 

—3.5 

1 

3  33  2 

1 

8  23.3 

1 

8    2.9 

1 

5  12.8 

4.8 

6.4 

—5.7 

-3.1 

2 

3  38.0 

2 

8  29.7 

2 

7  57.2 

2 

5     9.7 

5.6 

5.9 

—5.7 

'-3.7 

3 

3  43.G 

3 

3  35.G 

3    !     7  51.5 

3 

5    7.0 

6.4 

5.3 

—5.9 

-3.4 

4 

3  50.0 

4 

8  40.9 

4 

7  45,6 

4 

5    4.6 

+7.1 

+•1.6 

-6.0 

-1.9 

5 

3  57.1 

5 

8  45.5 

5 

7  39.G 

5 

5    2.7 

7.8 

4.0 

-6.0 

G 

4     4.9 

8.4 

6 

8  49.5     ^    g  4 

(i 

7  33.G 

-6.2 

6    I     5     1.1 

-I.I 

7 

4  13.3 

7 

8  52.9 

7 

7  27.4 

7 

5     0.0 

9.0 

2.8 

-0.3 

'  -0.7 

8 

4  22.3 

9.6 

8 

8  55.7 

2.3 

8        7  21.1 

-6.2 

o 

4  59.3 

-0.2 

9 

4  31.9 

9 

8  58.0 

9 

7  14.9 

9        4  59.1 

+10.3 

+1.7 

-6.4 

+0.2 

1881.0 

4  42.1 

1884.0 

8  59.7 

1887.0 

7    8.5 

1890.0        4  59.3 

10.7 

-6.4 

0.7 

1 

4  52.8 

1 

9     0.8     , 

1 

7    2.1 

1         5    0.0 

11.0 

0.7 

-6.4 

1.1 

2 

5    3.8 

2 

9     1.5 

2         G  55.7 

2 

5     1  1 

11.5 

+0.3 

-6.4 

1.6 

3 

5  15.3 

11.6 

3 

9     1.7 

-0.3 

3 

G  49.3 

-6.4 

3 

5    2.7 

2.1 

4 

5  2G.9 

4 

9     1.4 

4 

G  42.9 

4 

5    4.8 

+11.9 

-0.7 

-6.4 

+2.6 

5 

5  38.8 

5 

9    0.7 

5 

G  36.5 

5 

5    7.4 

13.0 

-1.2 

-6.4 

3.1 

6 

5  50.8 

G 

8  59.5 

G 

G  30.1 

(i 

5  10.5 

11.9 

-1.6 

-6.3 

3.5 

7 

6    2.7 

7 

8  57.9 

7 

6  23.8 

7 

5  14.0 

12.0 

-3.0 

-6.2 

4.0 

8 

G  14.7 

8 

8  55.9 

8 

6  17.6 

8 

5  18.0 

11.8 

-3.4 

-6.0 

4.4 

9 

G  2G.5 

9 

8  53.5 

9 

6  11.6 

9 

5  22.4 

+11.8 

-2.7 

-6.0 

+4.8 

1882.0 

G  38.3 

11.5 

1885.0 

8  50.8 

-3.1 

1888.0 

0    5.G 

-5.8 

1891.0 

5  27.2 

5.4 

1 

G  49.8 

1 

8  47.7 

1 

5  59.8 

1 

5  32.6 

11.3 

-3.3 

—  o.e 

5.8 

2 

7     1.1 

2 

8  44.4 

2         5  54.2 

2 

5  38.4 

10.9 

-3.7 

—5.5 

6.1 

3 

7  12.0 

3 

8  40.7 

3 

5  48.7 

3 

5  44.5 

10.6 

—3.9 

—5.4 

6.5 

4 

7  22.G 

4 

8  3G.8 

4 

5  43.3 

4 

5  51.0 

+10.2 

-4.3 

-5.1 

+6.9 

5 

7  32.8 

9.7 

5 

8  32.G 

-4.4 

5 

5  38.2 

-4.9 

5 

5  57.9 

7.2 

G 

7  42.5 

9.3 

G 

8  28.2 

-4.6 

G 

5  33.3 

-4.7 

6 

6    5.1 

7.5 

7 

7  51.8 

7 

8  23.6 

7 

5  28.6 

7 

6  12.6 

8.7 

-4.9 

-4.4 

7.8 

8 

8    0.5 

8 

8  18.7 

8 

5  24.2 

8 

6  20.4 

8.1 

-5.1 

—4.1 

8.0 

9 

8    8.G 

9 

8  13.G 

9 

5  20.1 

9 

G  28.4 

+  7.6 

-5.3 

-3.8 

+8.2 

1883.0 

8  1G.2 

1886.0        8    8.3 

1889.0 

5  16.3 

1892.0 

G  36.6 

THE    THIRD    SATELLITE. 


27 


TABLE  III. 


Perturbations  of  Jupiter  and  other  Inequalities. 


0,177759 


+  41)3.2 


+  (»)  S.ti23  sin  (5«  —  2  «.„  —  34.342)  —  (*)  5.775  sin  (II  — 


Years  and 
tenths. 

Years  and 

tenths. 

Perturb. 

Diff. 

Perturb. 

Diff. 

Years  ami 
tenths. 

Perturb. 

Diff. 

Years  and 
tenths. 

/ 

Perturb. 

Diff. 

in     s 

in      s 

m      s 

m     s 

181)2.0 

(i  36.6 

8 
+8.4 

1894.0 

9  14.2 

i 

+4.0 

1890.0 

9  23.9 

8 
-3.8 

1898.0 

7  38.6 

8 
-5.5 

1 

6  45.0 

8.6 

1 

9  19.1 

4.5 

1 

9  20.1 

-4.1 

1 

7  33.1 

-5.6 

2 

6  53.6 

8.7 

2 

9  23.6 

4.1 

2 

9  16.0 

-4.3 

2 

7  27.5 

-5.4 

3 

7    2.3 

8.8 

3 

9  27.7 

3.5 

3 

9  11.7 

-4.6 

a 

7  22.1 

-5.3 

4 

7  11.1 

4 

9  3'.2 

4 

9     7.1 

4 

7  16.8 

+8.8 

+3.1 

-4.8 

-5.2 

5 

7  19.9 

8.9 

5 

9  34.3 

2.6 

5 

9    2.3 

-5.1 

5 

7  11.6 

-5.1 

(j 

7  28.8 

8.9 

(i 

9  36.9 

2.1 

6 

8  57.2 

-fi.l 

(J 

7    0.5 

-4.9 

7 

7  37.7 

8.8 

7 

9  39.0 

1.5 

7 

8  52.1 

-5.3 

7 

7     1.0 

-4.8 

8 

7  40.5 

8.7 

8 

9  40.5 

1.1 

8 

8  40.8 

-5.5 

8 

6  56.8 

-4.6 

9 

7  55.2 

9 

9  41.6 

9 

8  41.3 

9 

6  52.2 

+8.6 

+0.6 

-5.4 

-4.4 

]  893.0 

8    3.8 

8.4 

1895.0 

9  42.2 

+0.1 

1897.0 

8  35.9 

-5.6 

1899.0 

6  47.8 

-4.3 

1 

8  12.2 

8.3 

1 

9  42.3 

-0.4 

1 

8  30.3 

-5.7 

1 

6  43.5 

-4.0 

.- 

a 

8  20.4 

7.9 

2 

9  41.9 

-0.8 

2 

8  24.6 

-5.7 

2 

6  39.5 

-3.9 

a 

8  28.3 

7.7 

3 

9  41.1 

-1.3 

3 

8  18.9 

-5.7 

3 

6  35.6 

-3.5 

4 

8  30.0 

4 

9  39.8 

4 

8  13.2 

4 

6  32.1 

+7.3 

-1.7 

-5.8 

-3.4 

5 

6  43.3 

6.9 

5 

9  38.1 

-2.1 

5 

8    7.4 

-5.8 

5 

6  28.7 

-3.1 

ti 

8  50.2 

6.6 

6 

9  36.0 

-2.5 

6 

8    1.6 

-5.8 

0 

6  25.6 

-a.s 

7 

8  56.8 

6.2 

7 

9  a3.5 

-2.9 

7 

7  55.8 

-5.7 

7 

6  22.8 

-2.5 

8 

9    3.0 

5.8 

8 

9  30.6 

-3.2 

8 

7  50.1 

-5.8 

8 

6  20.3 

-2.1 

i) 

!)    8.8 

9 

9  27.4 

9 

7  44.3 

9 

6  18.2 

+5.4 

-3.5 

-5.7 

-1.9 

189-1.0 

9  14.2 

1896.0 

9  23.9 

18J8.0 

7  38.6 

1900.0 

6  16.3 

• 

28 


THE   FOURTH 


TABLE  I. 


Epochs  of  the  Mean  Conjunctions 


YEARS. 

MEAN  CONJUNCTIONS. 

1 

2 

3 

4 

Days  and  parts  of  a  day, 
Paris  mean  civil  time. 

Fraction  of 
year. 

1880  B 

Jan.       h     m    s 
0       20  29     8.9 

0.002 

11     8706 

s.      o 
11  29.29 

s-      o 
9  11.75 

0  1(1.9 

1881 

3      10  21  41.3 

0.007 

0    9.329                 0     2.56 

8  11.37 

11   Ki.3 

1882 

7        0  14  13.7 

0.016 

1     9.951 

0    5.83 

7  1  6.96 

4  21.7 

1883 

10      14    G  46.2 

0.026 

2  10.573 

0    9.10 

6  19.55 

9  27.1 

1884  B 

14        3  59  18.6 

0.036 

3  11.196 

0  12.37 

5  22.18 

3    2.5 

1885 

10      17  51  51.0 

0.043 

4  11.818 

0  15.04 

4  24.83 

8     7.8 

1880 

3       13  39  16.5 

0.007 

5  11.048 

0    2.40 

3  12.37 

9  11.0 

1887 

7        3  31  48.9 

0.017 

6  11.670 

0    5.07 

2  15.05 

2  1(1.9 

1888  B 

10       17  24  21.3 

0.027 

7  12.293 

0    8.H4 

1   17.73 

7  22.2 

1889 

13        7  16  53.8 

0.034 

8  12.915 

0  12.21 

0  20.40 

0  27.5 

1890 

0        34  19.3 

0.000 

9  12.145 

11  28.97 

11     7.94                 2     1.2 

1891 

3      1C  56  51.7 

0.007 

10  12.708                0    2.24 

10  10.57 

7     0.6 

1892  B 

7        6  49  24.1 

0.017 

11  13.390                 0    5.51 

9  13.19                 0  12.0 

1893 

9      20  41  56.5 

0.024 

0  14.012                 0     8.78 

8  15.79                 5  17.4 

1894 

13      10  34  29.0 

0.034 

1    14.634 

0  12.05 

7  18.41 

10  22.8 

1895 

0        6  21  54.4 

0.000 

2  13.864 

11  28.81 

6    5.93 

11  26.5 

1896  B 

3      20  14  26.9 

0.008 

3  14.480                 0     2.C8 

5    8.58                 5     1.8 

1897 

6      10    6,59.3 

0.015 

4  15.109                 0    5.35 

4  11.  -20               10     7.2 

1898 

9      23  5J  31.7 

0.025 

5  15.731                 0    8.02 

3  13.93                 3  12.5 

1899 

13      13  52    4.1 

0.034 

0  16.353                 0  11.90 

2  10.00                 8  17.8 

1900 

0        93)  29.6 

0.000 

7  15.583               11  28.65 

1     4.14                 9  21.5 

SATELLITE. 


20 


and  the  Arguments  of  the  Inequalities. 


YKAKR. 

5 

6 

7 

I 

11 

11! 

IV 

1880  B 

»•   0 

4  9/2 

«•    0 

2  12.50 

*•    0 

1  20.1 

"•    0 

0  29.50 

>'•    0 

.  5  4.48 

42,?4 

8.    o 

0  11.0 

1881 

0  23/2 

3  12.45 

2  18.1 

2  0.16 

6  5.84 

5  24.6 

1  23.8 

188-2 

9  7.3 

4  12.43 

3  16/2 

3  0.85 

7  7/22 

6  27.9 

3  6.7 

1883 

5  21.4 

5  12.41 

4  14/2 

4  1.53 

8  8.60 

8  1.1 

4  19.6 

1884  B 

2  5.4 

6  12.35 

5  1-2.3 

5  2.18 

9  9.95 

9  4.4 

6  2.4 

1885 

10  19.2 

7  12.27 

6  10.3 

6  2.80 

10  11.27 

10  7.6 

7  15.2 

1880 

10  10.0 

8  10.82 

7  7.0 

7  2.02 

11  11.15 

1  1  9.2 

8  26.1 

1887 
1888  B 

C  29.8 
3  13.6 

9  10.71 
10  10.60 

8  4.9 
9  2.9 

8  2.62 
9  3.21 

0  12.44 
1  13.74 

0  12.4 
1  15.6 

10  8.8 
11  21.6 

1889 

11  27.4 

11  10.50 

10  0.9 

10  3.82 

2  15.C4 

2  18.8 

1  4.4 

1890 
1891 

11  24.2 

8  8.2 

0  9.05 
1  8.99 

10  27.6 
1  1  25.6 

11  3.04 
0  3.68 

3  14.93 
4  10.27 

3  20.5 
4  23.7 

2  15.3 
3  28.1 

181)2  B 

4  22.2 

2  8.94 

0  23.6 

1  4.34 

5  17.63 

5  26.9 

5  11.0 

1893 
1894 

1  6.2 

9  20.2 

3  8.91 
4  8.86 

1  21.7 
2  19.7 

2  5.01 
3  5.67 

6  18.99 
7  20.35 

7  0.2 
8  :>.4 

0  23.8 

8  6.7 

1895 
1896  B 

1897 

9  17.2 
6  1.0 
2  14.8 

5  7.43 
(i  7.34 
7  7.24 

3  16.4 
4  14.4 
5  12.4 

4  4.91 
5  5.53 
(i  6.13 

8  20.26 
9  21.57 
10  22.87 

9  5.1 
10  8.3 
11  1  1.5 

9  17.5 
11  0.4 
0  13.1 

1898 

10  28.6 

8  7.14 

6  10.4 

7  6.73 

11  24.17 

0  14.6 

1  25.9 

1899 

7  12.4 

9  7.04 

7  8.4 

8  7.34 

0  25.47 

1  17.8 

3  8.7 

1900 

7  9.2 

10  5.59 

8  5.1 

9  6.56 

1  25.36 

2  19.5 

4  n.(i 

30 


THE    FOURTH    SATELLITE. 


TABLE  III.  Perturbations  of  Jupiter  and  other  Inequalities. 


8  S  0  s 

l.llGiWSo  (.!_+  6  +  <5  E)  +  49X2  (0,  +  (5  »•)  +  (*)  la.odl  sin  (5  «  —  a  ua  —  3-1.512)  -f  l(j.(JD4  sin  (II  —  /Iv). 


Years  and      p         , 
tenths. 

Years  and 
tenths. 

Perturb. 

Diff. 

Years  and 
tenths. 

Perturb. 

Diff. 

Years  and 
tenths. 

Perturb. 

Diff. 

Diff. 

m     s 

m      s 

in      s 

in     s 

1880.0 

8  45.4 

s 

1883.0 

19  50.5 

s 

1880.0 

19  32.5 

s 

1889.0       12  49.0 

s 

+  9.5 

+16.3 

-12.9 

-  8.0 

] 

8  54.0 

1 

20  12.8 

1 

19  19.0 

1    '    12  41.0 

1  1.5 

14.9 

-13.3 

-  7.2 

2 

9    (i.4 

2 

20  27.7 

2 

19    (5.3 

2 

12  34.4 

13.3 

13.5 

—13.8 

-  6.4 

3 

9  19.7 

3 

20  41.2 

3 

18  52.7 

3 

12  28.0 

14.9 

12.0 

-i:i.  u 

—  5.4 

4 

9  34.0 

4 

20  53.2 

4 

18  38.8 

4 

12  22.0 

+16.8 

+10.7 

-14.1 

-  4.5 

5 

9  51.4 

5 

21     3.9 

5 

18  24.7 

5 

12  18.1 

18.3 

9.1 

-11.3 

-  3.6 

0 

10    9.7 

0 

21  13.0 

0 

18  10.4 

0 

12  14.5 

19.8 

7.8 

-14.5 

-  a.s 

7 

10  29.5 

7 

21  20.8 

7 

17  55.9 

7        12  12.0 

ai.a 

6.4 

-14.6 

-  1.5 

8 

10  50.7 

8 

21  27.2 

8 

17  41.3 

8 

12  10.5 

22.6 

5.1 

-1  1.7 

—  o.r> 

9 

11   13.3 

9 

21  32.3 

9 

17  20.0 

9 

12  10.0 

+23.8 

+  3.7 

-14.9 

+  0.6 

1881.0 

11  37.1 

1884.0 

21  30.0 

1887.0 

17  11.7 

]8:>o.o 

12  10.0 

25.1 

2.6 

-15.0 

I." 

1 

12    2.2 

1 

21  38.0 

1 

10  50.7 

1 

12  12.3 

26.0 

1.4 

-15.0 

2.8 

2 

12  28.2 

2 

21  40.0 

g 

1C  41.7 

2 

12  15.1 

26.7 

+  0.2 

-15.1 

3.8 

3 

12  54.9 

3 

21  40.2 

3 

10  20.0 

3 

12  18.9 

27.4 

-  0.9 

-15.0 

5.0 

4 

13  22.3 

4 

21  39.3 

4 

10  ll.fi 

4 

12  23.9 

+27.7 

-  2.0 

-15.0 

+  6.1 

5 

13  50.0 

27.9 

5 

21  37.3 

-  3.0 

5 

15  50.0 

-14.8 

5 

12  30.0 

7.2 

(i 

14  17.9 

C 

21.  34.3 

6 

15  41.8 

0 

12  37.2 

28.0 

-  3.9 

-14.7 

8.3 

7 

14  45.9 

7 

SI  30.4 

7 

15  27.1 

7 

12  45.5 

27.9 

-  4.9 

-14.4 

9.4 

8 

'  15  13.8 

8 

21  25.5 

8 

15  12.7 

8 

12  54.9 

27.7 

-  5.7 

-14.2 

10.4 

9 

15  41.5 

9 

21   19.8 

9 

14  58.5 

9 

13     5.3 

+27.3 

-  6.6 

-14.0 

+11.5 

1882.0 

10    8.8     |     „. 

1685.0 

21   13.2 

18S8.0 

14  44.5 

1891.0 

13  10.8 

ab.y 

-  7.2 

-13.5 

12.5 

1 

10  35.7 

1 

21     C.O 

1 

14  31.0 

1 

13  29.3 

26.3 

-  8.0 

-13.3 

13.5 

2 

17    2.0 

2 

20  58.0 

2 

14  17.7 

2 

13  42.8 

25.fi 

—  8.7 

-12.8 

14.4 

3 

17  27.5 

3 

20  49.3 

3 

14     4.9 

3 

33  57.2 

24.7 

-  9.4 

-12.4 

15.3 

4 

17  52.2 

4 

20  39.9 

4 

13  52.5 

4 

14  12.5 

+33.6 

-  9.9 

-11.9 

+16.1 

5 

18  15.8 

5 

20  30.0    I 

5 

13  40.0 

5 

14  28.0 

23.6 

1     -10.5 

-11.5 

16.8 

<; 

18  38.4 

(i 

20  19.5 

0 

13  29.1 

0 

14  45.4 

21.4 

-11.0 

-10.8 

17.6 

7 

18  59.8 

7 

20    8.5 

7 

13  18.3 

7 

15    3.0 

20.2 

-11.6 

-10.3 

18.1 

8 

19  20.0 

8 

19  50.9 

8 

13    8.0 

8 

-15  21.1 

18.9 

-12.0 

-  9.5 

18.7 

9 

19  38.9 

9 

19  44.9 

9 

12  58.5 

9      15  39.8 

+17.6 

-12.4 

-  8.9 

+19.9 

1883.0 

19  50.5 

188C.O 

19  32.5 

1889.0 

12  49.0 

1892.0       15  59.0 

THE    FOURTH    SATELLITE. 


31 


TABLE  III.  Perturbations  of  Jupiter  and  other  Inequalities. 


S  S  0  8 

1.1160035  (J  +  0  +  (!  E)  +  493.2  (Ji  +  <!r)  +  (*)  15.581  sin  (5  a  —  2  «„  —  34.542)  +16.694  sin  (II 


I 

Years  and 
tenth*. 

Perturb. 

Diff. 

Years  and 

telltllS. 

Perturb. 

Diff. 

Years  and 
tentlis. 

Perturb. 

Diff. 

Years  and 
tenths. 

Perturb. 

Diff. 

11]       S 

Ill       S 

Ill       S 

Ill       S 

1892.0 

15  59.0 

i 

+19.6 

1894.0 

22    5.0 

P 
+11.1 

1896.0 

2>  24.2 

S 

-  9.1 

1898.0 

18  15.7 

s 
-13.2 

1 

16  18.fi 

20.0 

1 

22  16.4 

10.4 

1 

22  15.1 

-  9.7 

1 

18    2.5 

-13.0 

2 

1C  38.C 

20.3 

2 

22  26.8 

9.9 

2 

22    5.4 

-10.3 

2 

17  49.5 

-12.7 

a 

16  58.9 

90.5 

3 

22  36.0 

8.9 

3 

21  55.1 

-10.9 

3 

17  36.8 

-12.5 

4 

17  19.4 

4 

22  44.2 

4 

21  41.2 

4 

17  24.3 

1 

+30.6 

+  7.0 

-11.3 

-12.1 

5 

17  40.0 

20.7 

5 

22  51.2 

5.9 

5 

21  32.9 

-11.8 

5 

17  12.2 

-11.9 

6 

18    0.7 

20.7 

6 

22  57.1 

4.6 

6 

21  21.1 

-19.2 

6 

17     0.3 

-11.6 

• 

7 

18  21.4 

20.5 

7 

23     1.7 

3.5 

7 

21     8.9 

-19.5 

7 

16  48.7 

-11.9 

8 

18  41.9 

20.9 

8 

23    5.2 

2.3 

8 

20  56.4 

-13.8 

8 

16  37.5 

-10.8 

9 

19    2.1 

9 

23    7.5 

9 

20  43.6 

9 

16  26.7 

. 

+19.9 

+  1.9 

-la.i 

-10.4 

1893.0 

19  22.0 

19.6 

1895.0 

23     8.7 

0.0 

1897.0 

20  30.5 

-13.9 

1899.0 

16  16.3 

-  9.9 

1 

19  4I.C) 

1 

23     8.7 

1 

20  17.3 

1 

16    6.4 

18.9 

-  1.1 

-13.3 

-  9.4 

2 

20    0.5 

18.4 

2 

23    7.6 

-  9.1 

2 

20     4.0 

-13.5 

2 

15  57.0 

-  9.0 

3 

20  18.9 

3 

23    5.5 

3 

19  50.5 

3 

15  48.0 

17.7 

-  3.6 

-13.5 

-  8.3 

4 

20  30.6 

4 

23     1.9 

4 

19  37.0 

4 

15  39.7 

+17.0 

-  3.8 

-13.6 

-  7.8 

5 

20  53.6 

16.1 

5, 

22  58.1 

-  5.1 

5 

19  23.4 

-13.6 

5 

15  31.9 

-  7.2 

(i 

21     9.7 

15.9 

6 

'22  53.0 

-  6.0 

6 

19    9.8 

-13.6 

6 

15  24.7 

-  6.5 

7 

21  24.9 

7 

22  47.0 

7 

18  56.2 

7 

15  18.2 

14.4 

-  6.8 

-13.6 

-  5.8 

8 

21  39.3 

8 

22  40.2 

8 

18  42.6 

8 

15  12.4 

13.3 

-  7.7 

-13.5 

-  5.1 

9 

21  52.6 

9 

22  32.5 

9 

18  29.1 

9       15     7.3 

+19.4 

-  8.3 

-13.4 

-  4.3 

1894.0 

22    5.0 

1896.0 

22  24.2 

1898.0 

18  15.7 

1900.0       15    3.0 

TABLE    A. 


LONGITUDES    OF    OBSERVATORIES. 


West  longitudes,  positive. 


Place  of  Observatory. 

Longitude  from 
Paris. 

Place  of  Observatory. 

Longitude  from 
Paris. 

0 

Abo 

li     in      R 
—  1   19  47.3 
+  54  20.3 
+  5  29  23.8 
—  0  30  25.1 
+  5  44  10.2 

+  0  35  5(5.5 
—  1  25  34.1 
—  0  44  14.3 
—  0  17  44.3 
—  0  19    3.0 

—  0  58  48.7 
—  0    8     7.8 
4-08  58.4 
+  4  53  52.0 
1     4  34.6 

li      in     s 
+  0  21  21.1 
—  511  30.2 
+  0  24     0.4 
—  0  24  30.0 
+  0  43    9.4 

—  0  12    7.5 
—  0  27  25.2 
—  0  34  22.5 
—  2  20  55.8 
—  0  37     5.0 

—  0  47  37.9 
+  5    5   17.7 
I  58  33.1 

Mtttlras   

Bilk                                              .     .     . 

Naples    

—  0  59  42.4 
+  0  14  23.7 

—  0  38     8.2 
—  0  44     4.0 
9  54  45.2 

Oxford    

+  5  59  47.8 
—  0  33  33.2 
+  5  47  20.1 
+  5  10  58.5    ' 
—  0  40  57.0 

+  4  £6    6.0 
—  1   10  29.8 
—  1  37  33.0 
+  0  34  43.1 
+  0  15  40.8 

+  022    4.1 
—  0  35  42.1 
—  0  15  Ki.2 
+  5  17  39.4 
—  0  30  25.5 

—  0  33  29.9 
+  0    9  21.1 
—  0  30  32.5 
—  1  30  28.3 
+  5  35    5.2 

—  37    7.7 
—  1  12  38.4 
—  0  47  12.0 
—  0  40  13.4 
—  08  35.1 

+  5     9  59.5 
—  0  48  20.5 

1   51  57.0 

Copenhagen     

Koine      

—  0  40  35.1 
+  0  34  10.1! 
+  4  52    3.4 
—  0  50  29.0 

—  0  24  25.0 
—  I     2  53.3 
—  1  51  52.1 
—  1     1     9.7 
—  Oil   10.0 

—  0  50  11.1 
+  5  17  33.2 
-1  31  50.3 

Dublin         

St  Petei'sbnr"      

Utrecht   

Gotha           

Wilnii     

Koenigsber*;    
Ivremsmnenster  

Leyden  .         

TABLES 


FOR 


FINDING    THE    CONFIGURATIONS 


OF    THE 


SATELLITES  OF  JUPITER. 


34 


THE    FIRST    SATELLITE. 


TABLE  I.      Epochs  of  the  Mean  Longitude,  and  the  Arguments  of  the  Inequalities, 

for  January  1,  Pans  menu  midnight. 


YEARS. 

Mean  Longitude. 

1 

.   2 

3 

4 

5 

1880  B 

S.     o 

6   9.80 

8.     0 

9  19.2 

S.      o 

11   8.4 

0  0?8 

*•     0 

2   5.9 

"•     0 

7  24.6 

1881 

4  26.77 

8  19.5 

0   8.8 

0  1.0 

1  1  29.7 

6  11.5 

1882 

8  20.25 

7  18.9 

1   9.1 

0  1.3 

6  11.4 

10   5.0 

1883 

0  13.73 

6  18.4 

2   9.5 

0  1.1 

0  23.1 

1  28.5 

1884  B 

4   7.21 

5  17.8 

3   9.8 

0  0.8 

7   4.8 

5  22.0 

1885 

2  24.18 

4  18.1 

4  10.2 

0  1.6 

4  28.6 

4   8.9 

1886 

6  17.67 

3  17.5 

5  10.5 

0  1.3 

1  1  10.3 

8   2.4 

1887 

10  11.15 

2  16.9 

6  10.8 

0  1.1 

5  22.0 

11  25.9 

1888  B 

2   4.63 

1  16.4 

7  11.2 

0  0.8 

0   3.7 

3  19.4 

1889 

0  21.61 

0  16.7 

8  11.6 

0  1.6 

9  27.5 

2   6.3 

1890 

4  15.09 

11  16.1 

9  11.9 

0  1.3 

4   9.2 

5  29.8 

1891 

8   8.57 

10  15.5 

10  12.2 

0  1.1 

10  20.9 

9  23.2 

1892  B 

0   2.05 

9  14.9 

1  1  12.6 

0  0.8 

5   2.6 

1  16.7 

1893 

10  19.03 

8  15.3 

0  13.0 

0  1.6 

2  26.4 

0   3.6 

1894 

2  12.51 

7  14.7 

1  13.3 

0  1.3 

9   8.1 

3  27.1 

1895 

6   5.99 

6  14.1 

2  13.6 

0  1.1 

3  19.8 

7  20.6 

189(5  B 

9  29.47 

5  13.5 

3  14.0 

0  0.8 

10   1.5 

11  14.1 

1897 

8  16.45 

4  13.8 

4  14.4 

0  1.5 

7  25.3 

10   1.0 

1898 

0   9.93 

3  13.3 

5  14.7 

0  1.2 

2   7.0 

1  24.5 

1899 

4   3.41 

2  12.7 

6  15.0 

0  1.0 

8  18.7 

5  17.9 

1900 

7  26.89 

1  12.1 

7  15.3 

0  0.8 

3   0.4 

9  11.4 

THE    SECOND    SATELLITE. 


35 


TABLE  I.     Epochs  of  the  Mean  Longitude,  and  the  Arguments  of  the  Inequalities, 

lor  January  1,  Paris  mean  midnight. 


YEARS. 

Mean 
Longitudf. 

1 

2 

3 

4 

K 

6 

7 

1880  B 

s-    0 

4  3.87 

*•   0 

9  19.2 

8.   0 

11  8.4 

S.   o 

0  0.8 

S.    o 

10  2.9 

"•    0 

5  18.7 

"•    0 

5  0.2 

»•    0 

9  10.6 

1881 

4  27.04 

8  19.5 

0  8.8 

0  1.6 

8  29.8 

6  1  1.8 

6  5.4 

10  6.3 

1883 

a  8.82 

7  18.9 

1  9.1 

0  1.3 

6  5.7 

3  23.6 

3  29.3 

7  20.6 

1883 

1  1  20.61 

ti  18.4 

2  9.5 

0  1.1 

3  11.5 

1  5.4 

1  23.1 

5  4.9 

1884  B 

9  2.40 

5  17.8 

3  9.8 

0  0.8 

0  17.4 

10  17.2 

11  17.0 

2  19.3 

1885 

9  25.56 

4  18.1 

4  10.2 

0  1.6 

11  14.3 

11  10.3 

0  22.2 

3  15.0 

1886 

7  7.35 

3  17.5 

5  10.5 

0  1.3 

8  20.1 

8  22.1 

10  16.0 

0  29.3 

1887 

4  19.14 

2  16.9 

6  10.8 

0  1.1 

5  26.0 

6  3.9 

8  9.9 

10  13.6 

1888  B 

2  0.93 

1  16.4 

7  11.2 

0  0.8 

3  1.8 

3  15.6 

6  3.7 

7  27.9 

1889 

2  24.09 

0  16.7 

8  11.6 

0  1.6 

1  28.7 

4  8.8 

7  9.0 

8  23.7 

1890 

0  5.88 

11  16.1 

9  11.!) 

0  1.3 

11  4.6 

1  20.6 

5  2.8 

6  8.0 

1891 

9  17.67 

10  15.5 

10  12.2 

0  1.1 

8  10.4 

1  1  2.3 

2  26.7 

3  22.3 

1892  B 

0  29.45 

9  14.9 

11  12.6 

0  0.8 

5  16.3 

8  14.1 

0  20.5 

1  6.6 

1893 

7  22.62 

8  15.3 

0  13.0 

0  1.6 

4  13.2 

9  7.3 

1  25.8 

2  2.3 

1894 

5  4.41 

7  14.7 

1  13.3 

0  1.3 

1  19.0 

6  19.0 

11  19.6 

11  16.7 

1895 

2  16.19 

6  14.1 

2  13.6 

0  1.1 

10  24.9 

4  0.8 

9  13.5 

9  1.0 

1896  B 

11  27.98 

5  13.5 

3  14.0 

0  0.8 

8  0.7 

1  12.6 

7  7.3 

6  15.3 

1897 

0  21.14 

4  13.8 

4  14.4 

0  1.5 

(i  27.6 

2  5.7 

8  12.6 

7  11.0 

1898  ' 

10  2.93 

3  13.3 

5  14.7 

0  1.2 

4  3.5 

11  17.5 

6  6.4 

4  25.4 

1899 

7  14.72 

2  12.7 

6  15.0 

0  1.0 

1  9.3 

.   8  29.3 

4  0.2 

2  9.7 

1900 

4  26.51 

1  12.1 

7  15.3 

0  0.8 

10  15.2 

6  11.0 

1  24.1 

11  24.0 

36 


THE    THIRD    SATELLITE. 


TABLE  I.    Epochs  of  the  Mean  Longitude,  and  the  Arguments  of  the  Inequalities, 

for  January  1,  Paris  mean  midnight- 


YEARS. 

Mean 
Longitude. 

1 

2 

3 

4 



5 

6 

7 

8 

9 

1880  B 

8.    0 

6  0.92 

S.    o 

9  19.2 

S.    0 

11  8.4 

8.   o 

0  0.8 

B.    o 

10  2.9 

8.    o 

8  5.5 

8-    0 

8  28.0 

8-    0 

7  15.8 

s.   0 
11  7.6 

8-    0 

11  20.7   . 

1881 

7  27.18 

8  19.5 

0  8.8 

0  1.6 

8  29.8 

9  29.1 

10  23.6 

9  12.0 

1  6.4 

1  17.7 

1882 

8  3.12 

7  18.9 

1  9.1 

0  1.3 

6  5.7 

10  2.5 

10  28.8 

9  18.0 

1  14.9 

I  24.3 

1883 

8  9.06 

6  18.4 

2  9.5 

0  1.1 

3  11.5 

10  5.8 

11  4.0 

9  23.9 

1  23.4 

2  0.9 

1884  B 

8  15.00 

5  17.8 

3  9.8 

0  0.8 

0  17.4 

10  9.1 

11  9.3 

9  29.9 

2  1.9 

2  7.6 

1885 

10  11.26 

4  18.1 

4  10.2 

0  1.6 

11  14.3 

0  2.7 

1  4.8 

11  26.0 

4  0.7 

4  4.5 

1886 

10  17.20 

3  17.5 

5  10.5 

0  1.3 

8  20.1 

0  6.1 

1  10.1 

0  2.0 

4  9.2 

4  11.1 

1887 

10  23.14 

2  16.9 

6  10.8 

0  1.1 

5  26.0 

0  9.4 

1  15.3 

0  8.0 

4  17.6 

4  17.7 

1888  B 

10  29.08 

1  16.4 

7  11.2 

0  0.8 

3  1.8 

0  12.7 

1  20.5 

0  13.9 

4  26.1 

4  24.3 

1889 

0  25.34 

0  16.7 

8  11.6 

0  1.6 

1  28.7 

2  6.3 

3  16.1 

2  10.1 

6  24.9 

6  21.3 

1890 

1  1.28 

11  16.1 

9  11.9 

0  1.3 

11  4.6 

2  9.7 

3  21.3 

2  16.0 

7  3.4 

6  27.9 

1891 

1  7.22 

10  15.5 

10  12.2 

0  1.1 

8  10.4 

2  13.0 

3  26.5 

2  22.0 

7  11.9 

7  4.5 

1892  B 

1  13.16 

9  14.9 

11  12.6 

.  0  0.8 

5  16.3 

2  16.3 

4  1.7 

2  27.8 

7  20.4 

7  11.1 

1893 

3  9.42 

8  15.3 

0  13.0 

0  1.6 

4  13.2 

4  10.0 

5  27.3 

4  24.2 

9  19.2 

9  8.1 

1894 

3  15.36 

7  14.7 

1  13.3 

0  1.3 

1  19.0 

4  13.3 

6  2.5 

5  0.0 

9  27.6 

9  14.7 

1895 

3  21.30 

6  14.1 

2  13.6 

0  1.1 

10  24.9 

4  16.6 

6  7.8 

5  6.0 

10  6.1 

9  21.3 

1896  B 

3  27.24 

5  13.5 

3  14.0 

0  0.8 

8  0.7 

4  19.9 

6  13.0 

5  11.9 

10  14.6 

9  27.9 

1897 

5  23.50 

4  13.8 

4  14.4 

0  1.5 

6  27.6 

6  13.6 

8  8.5 

7  8.2 

0  13.4 

11  24.9 

1898 

5  29.44 

3  13.3 

5  14.7 

0  1.2 

4  3.5 

6  16.9 

8  13.7 

7  14.0 

0  21.9 

•  0  1.5 

1899 

6  5.38 

2  12.7 

6  15.0 

0  1.0 

1  9.3 

6  20.2 

8  18.9 

7  20.0 

1  0.4 

0  8.1 

1900 

6  11.32 

1  12.1 

7  15.3 

0  0.8 

10  15.2 

6  23.5 

8  24.2 

7  25.9 

1  8.8 

0  14.7 

THE    FOURTH    SATELLITE. 


37 


TABLE  I.     Epochs  of  the  Mean  Longitude,  and  the  Arguments  of  the  Inequalities, 

for  January  1,  Paris  mean  midnight. 


YEARS. 

Mean 
Longitude. 

1 

2 

3 

4 

5 

6 

7 

1880  B 

"•    0 

11  17.40 

9  19?2 

8.    0 

11  8.4 

0  0.8 

*•    0 

2  14.4 

S.    o 

1  2.2 

8.    0 

5  7.2 

8.    o 

4  24.1 

1881 

10  22.42 

8  19.5     0  8.8 

0  1.6     1  18.7 

0  7.2     4  12.9 

4  1.6 

1882 

9  5.88 

7  18.9 

1  9.1 

0  1.3 

0  1.5 

10  20.7 

2  27.0 

2  17.6 

1883 

7  19.33 

6  18.4 

2  9.5 

0  I.I 

10  14.2 

9  4.1 

1  11.2 

1  3.6 

1884  B 

C  2.79 

5  17.8 

3  9.8 

0  0.8     8  27.0 

7  17.6    11  25.3 

11  19.6 

1885 

5  7.81 

4  18.1 

4  10.2 

0  1.6     8  1.3     6  22.6 

11  1.0 

10  27.2 

1886 

3  21.27 

3  17.5 

5  10.5 

0  1.3     6  14.0     5  6.0     9  15.1 

9  13.2 

1887 

a  4.72     2  16.9     6  10.8 

0  1.1     4  26.8 

3  19.4     7  29.3 

7  29.2 

1888  B 

0  18.18     1  16.4     7  11.2 

0  0.8     3  9.5     2  2.9 

6  13.4 

6  15.2 

1889 

11  23.20     0  16.7     8  11.  <i 

0  1.6     2  13.8     1  7.9     5  19.1 

5  22.7 

1890 

10  6.66 

11  16.1     9  11.9 

0  1.3     0  26.5    11  21.3     4  3.2 

4  8.7 

1891 

8  20.11 

10  15.5 

10  12.2 

0  1.1     11  9.3    10  4.8 

2  17.4 

2  24.7 

1892  B 

7  3.57 

9  14.9 

11  12.6 

0  0.8 

9  22.0 

8  18.2 

1  1.5 

1  10.7 

1893 

6  8.60 

8  15.3 

0  13.0 

0  1.6     8  26.4 

7  23.2 

0  7.2 

0  18.3 

1894 

4  22.05 

7  14.7 

1  13.3 

0  1.3 

7  9.1 

6  6.7 

10  21.3 

11  4.3 

1895 

3  5.50 

6  14.1 

2  13.6 

0  1.1 

5  21.8 

4  20.1 

9  5.5 

9  20.3 

1896  B 

1  18.96 

5  J3.5 

3  14.0 

0  0.8 

4  4.6     3  3.6     7  19.6 

8  6.3 

1897 

0  23.99 

4  13.8 

4  14.4 

0  1.5 

3  8.9     2  8.6 

6  25.3 

7  13.8 

I 

. 

' 

1898 

1  1  7.44 

3  13.3 

5  14.7 

0  1.2     1  21.6     0  22.0     5  9.4 

5  29.8 

1899 

9  20.90 

2  12.7 

6  15.0 

0  1.0     0  4.4    11  5.4     3  23.6 

4  15.8 

1900 

8  4.35 

1  12.1 

7  15.3 

0  0.8 

10  17.1 

9  18.9 

2  7.7 

3  1.8 

CORRECTIONS  TO  THE 


TABLES  ECLIPTIQUES  DBS  SATELLITES  DE  JUPITER,  ETC., 


PAR  LE  BARON  DE  DAMOISEAU,  PARIS,  1836. 


Page. 

(Ill),  tenth  line  from  the  bottom, 

(iv),  second  line, 

(V),  tt,,  — Mm. 

(VI),  Table  X,  third  term, 

(vil),  eighteenth  line, 

( vil),  eleventh  line  from  the  bottom, 

(VII),  Table  XII, 

(VIII),  Table  XXV, 

(VHI),  Tables  XXVIII— XXXII, 

(VIIl),  II — «0  , 

(ix),  Table  XII,  third  term, 

(x),  twelfth  line, 

(XIV),  ninth  line  from  the  bottom, 

(XIV ),  sixth  line  from  the  bottom, 

(XVll),  nineteenth  line, 

2,  Conjunctions  Moyennes,  1755, 

6,  Conjonctions  Moyennes,  1847, 

7,  Arg.  5,1848, 

9,  Arg.  5,  Janvier  14, 

10,  Arg.  4,  Mars  6, 

10,  Arg.  3,  Avril  23, 

11,  Arg.  8,  Fe>rier  6, 

12,  Arg.  1,  Mai  5, 
12,  Arg.  1,  Mai  25, 

14,  Arg.  1,  Juillet  29, 

15,  Arg.  9,  Septemb.  22, 
If),  Arg.  I,  Septemb.  22, 

16,  Revolutions,  Octobre  27, 

17,  Arg.  V,  Novemb.  25, 
25,  Diff.  1847,2  to  1847,3, 
20,  Perturb.  1H60,1, 

32,  I'  4°, 

32,  X-  16°, 

33,  Vs  Equation  22°, 
35,  I'Diff.  28°  to  29°, 
35,  IIs  Diff.  26°  to  30°, 

35,  III-  Diff.  17°  to  18°, 

36,  Arg.  1,  III"  20°,  Arg.  3,  XIs  0°  to  30°, 

37,  Arg.  1,  VI"  0°,  Arg.  3,  XI'  10°, 

38,  Arg.  a,  IP  0°,  Arg.  3,  IX'  20°, 

39,  top  of  page, 

39,  Arg.  a,  XI-  10°,  Arg.  3,  I"  0°, 


for    «'  —  2  uu  +  Tn, 

read 

«,  —  2u,,  +  -m 

for     I,  II,  III,  IV.  relativement 

read 

1.  II.  Ill,  relativement 

for     11.  27,7519 

read 

HI.  27.7519 

for    +0"2,18cos(l)cos3[3—  E+E'] 

read 

+  0",218  cos  (  1  )  cos  3  [  3—  E  +E'  ] 

for    um  —  Tm  +  1,0015  0 

read 

«.,„  —  5rm  +  1,0016  4 

for    +i.~i  D"  51)' 

read 

+  i  .  7J  3h  59' 

for    —  0",115cos2(8) 

read 

—  0",115eos(8) 

for    —0,008979  .  sin  (III  +  1.0026  K) 

read 

—  0,008979  .  sin  (III  +  1.0016  E) 

for    N  =  2P  —  P 

read 

N  =  2P  —  P-> 

for    9.     6,  1550 

read 

9.  8,1550 

for    +  0"2,18cos(l)cos3[3—  E+E'] 

read 

+  0",218  COB  (1)  cos  3[3—  E+E 

'1 

for    XIX 

read 

XXIX 

for     les  tables  XXIII—  XXVI 

read 

l.'s  tables  XXIII—  XXVII 

for    la  table  XXVII 

read 

la  table  XXVIII 

for    2I  +  VI 

read 

aI  +  6 

for    1        10.  26.  28,1 

read 

1        10.  26.  8,1 

for    2        0.  8.  27,1 

read 

2        0.  8.  27,0 

for    3.  24,6 

read 

3.  25,6 

for    0.     6,7 

read 

0.     8,7 

/or    6.  26,98 

read 

6.  26,93 

for    3.  12,93 

read 

3.  12,23 

/or     0«27°,0 

read 

0»  27°,8 

for    2.  10,441 

read 

0.  10,441 

/or     1.  12,058 

read 

0.  12,058 

for    0.  17,490 

read 

0.  17,499 

for    6.  16,3 

read 

6.  16,8 

/or    0.   22,08 

read 

0.  22,06 

for    21.  1.  51,7 

read 

21.  1.  50,7 

for    1.  26,7 

read 

0.  26,7 

/or    0,6 

rmd 

0,7 

for    2.  27,9 

read 

2.  JL7,9 

/or    2,01 

read 

3,01 

for    0,55 

read 

0.57 

/or    0.  46.  15,6 

read 

0.  46.  13,6 

for    6,5 

read 

6,6 

/or    8,3   8,3   8,2   8,1 

read 

8,4   8,4   8,4   8,4 

/or     3,5 

read 

,8,5 

for     1,5     1.5     1.5     1,4 

read 

1,6     1,6    1,6     1,6 

for    2,0 

read 

2,1 

/or    6,6 

read 

6,2 

/or     Suite  de  la  TABLE  XI 

read 

Suite  d«  la  TABLE  XII 

for    1,8 

read 

1,3 

CORRECTIONS    TO    DE  DAMOISEAll'S   TABLES    ECLIPTIQUES,    PARIS,    1836. 


39 


Page, 

•  41, 

top  of  |>ilge. 

42, 

heading  of  second  column, 

43, 

Is  R&luct.  23°, 

44, 

III"Nombre20°, 

45. 

Arg.  0,4000,  P, 

53, 

Arg.  1,  1838, 

58, 

Revolutions,  Novcnil).  15. 

72, 

\'  Eolation  27°, 

7:!, 

IX8  Diff.  20°  to  21°, 

75. 

Arg.  1,  0"  20°,  Arg.  3,  VIIIs  0°, 

75, 

Arg.  1,  V"  10°,  Arg.  3,  IVs  10°. 

75, 

Arg.  1,  V  10°,  Arg.  3,  IV  20°, 

78, 

Arg.  I,  Xs  20°,  Arg.  3,  IX-  20°, 

76, 

Arg.  1,  XI"  10°,  Arg.  3,  X-  0°, 

78, 

Arg.  2,  VI"  20°,  Arg.  3.  Ill"  10°, 

80, 

IX"  Squat.  15°, 

ar>, 

III»l)iif.  3cto5°, 

88, 

Arg.  1,1400  to  1,1500,  Diff., 

92, 

Conjonctione  Moyennes,  1769, 

93, 

Arg'.  9,  1772, 

96, 

Arg.  3,  1863, 

97, 

Arg.  8,  1857, 

97, 

Ar-  11,1857, 

98, 

Arg.  5,  1867, 

98, 

Arg.  5,  Miii  1, 

98, 

Arg.  5,  Mai  8, 

99, 

Arg.  IV,  1877, 

100, 

Arg.  5.  Mai  10. 

109, 

Diff.  1869,6  to  1869,7, 

111, 

VIII"  16°, 

111, 

IX6  16°, 

115, 

first  column, 

118, 

Arg.  1,  V  20°,  Arg.  3,  X"  0°, 

119, 

Arg.  1,VI"10°,  Arg.  3,  II"  0°, 

119, 

Arg.  1,  VIIIs  10°,  Art.  3,  0>20°, 

119, 

Arg.  1,  XI"  0°,  Arg.  3,  V"20°, 

121, 

Arg.  2,  VI"  20°,  Arg.  3,  IIIs  10°, 

122, 

IIIs  Squat.  11°, 

122, 

IIIs  Diff.  10°  to  12°, 

123, 

Xs  Squat.  6°, 

123, 

VIP  Squat.  15°, 

124, 

top  of  columns  0"  —  XIs, 

125, 

first  column. 

125, 

0s  Equation  1°, 

126, 

VIII"  Equation  11°, 

127, 

IV"  Diff.  27°  to  28°, 

127, 

VIII"  Diff.  0°  to  1°, 

129, 

V"  R&luct.  3°, 

133, 

VI"  Nombre  8°, 

134, 

V"  20°, 

135, 

VIII"  16°, 

135, 

VIII"  17°, 

136, 

Arg.  0,16000,  Demi-dnre'es, 

136, 

second  column  of  Arg., 

130, 

Arg.  0,46000,  N, 

far  Suite  de  la  TABLE  V 

for  Argument  3 

for  0,7 

for  0,5700 

for  1000 

for  10.  0,9 

for  20.  50.  36,3 

for  1.  24.  36,6 

for  23,7 

for  2,1 

for  0,3 

for  1,6 

for  1,9 

for  1,5 

for  9,7 

for  22.  32,2 

for  5     6 

for  3      2 

for  5        0.     9.- 33,8 

for  4.     3,2 

for  3.  23,33 

for  7.  28,8 

for  3.  16,96 

for  8.  23,8 

for  8.     2 

for  3.     2,1 

for  S.     4,3 

far  14",2 

for  10,1 

for  0,1 

for  0,3 

far  0°  4    3    2     1    5 

for  1,6 

for  1,6 

far  2,0 

for  0,5 

for  9,7 

far  4.  5,4     . 

far  0,5    0,4 

far  0.  21,1 

for  0.  37,7 

for  27°,9,    8°,7,  etc. 

for  0°  4    3    2    1     5 

far  4.  12,2 

for  8.  23,3 

far  1,1 

far  0",7 

far  2.  41,8 

far  0,01028 

for  0,02547 

far  7,00352 

for  0,0«352 

for  1.     6.  31,2 

for  0,3100,     0,3200,     0,3300,  etr. 

for  0,62 


read 

Suite  de  la  TABLE  XIII 

read 

Argument  5 

read 

0,9 

read 

0,6700 

read 

1,00 

read 

10.  5,9 

read 

20.  50.  36,2 

read 

1.  24.  26,6 

read 

22,7 

read 

2,2 

read 

0,6 

read 

1,0 

read 

M 

read 

1,3 

read 

8,5 

read 

22.  33,2 

read 

6    7 

read 

30,2 

read 

5        0.    9.  43,8 

read 

4.  13,2 

read 

2.  23,33 

read 

2.  28,8 

read 

3.  15,% 

read 

4.  23,8 

read 

8.  22,1 

read 

3.  18,2 

read 

8.     5,3 

read 

14°,2 

read 

10,0 

read 

0,3 

read 

0,1 

read 

0°  1    2    3    4    5 

read 

1,4 

read 

1,4 

read 

2,1 

read 

0,6 

read 

8,5 

read 

4.     5,5 

read 

0,4    0,5 

read 

0.  21,0 

read 

0.  36,7 

read 

27",9,     8",7,  etc. 

read 

0°  1    2    3    4    5 

read 

4.  14,2 

read 

8.  23,1 

read 

0,9 

read 

0",5 

read 

2.  41,0 

read 

0,01023 

read 

0,00547 

read  0,00352 

read  0,00352 

read  I.     6.  51,2 

read  0,31000,     0,32000,     0,33000,  etc. 

read  0,61  " 


40 


CORRECTIONS   TO    DE  DAMOISEAU'.S    TABLES    ECLIPTIQUES,    PARIS,    1836. 


Page. 

138,     top  of  page, 

146,    Arg.  3,  1840  B, 


149,     Arguments  I  and  II,  1866  to  1880  B, 


149,  Arg.  Ill,  1878, 

164,  first  column, 

166,  IIs  Diff.  10°  to  11°, 

167,  Arg.  1,  I-  20°,  Arg.  3,  X-  0°, 
167,  Arg.  1,  IV  20°,  Arg.  3,  VII- 10°, 

167,  Arg.  1,  I Vs  20°,  Arg.  3,  VIIs  20°, 

170,  Arg.  2,  VIs  20°,  Arg.  3,  III'  10°, 

171,  VIIIs  19°, 
177,  III'  20°, 

180,  first  column, 

181,  Arg.  0,50000  to  0,51000,  Diff., 
183,  IIs  Diff.  27°  to  28°, 

183,  IV  Diff.  10°  to  11°, 

184,  second  column  of  Arg.  Q  +  Z, 

187,  Arg.  Q  -f  Z,  0,64000  to  0,65000,  Diff., 

(190),  X"  Equation  27°, 

(193),  eleventh  line, 

(216),  Longit.  moy.,  1849, 


(224),    Argument  4,  1870  to  1880  B, 


for    Suite  de  la  TABLE  XVIII 
for    1.  26,92 


for    +11.     5  ,7 

for    l'61ongation  est  entre  3'  et  0' 

for    4.  5,32 

4.  23,0 

3.     5,7 

1.  18,5 

0.  22,8 
11.    5,5 


for 


read    Suite  de  la  TABLE  XXVIII 
read    1.  26,62 


'  10s  24,50 

2«  13,50  i 

W  25,00 

2-  20,30  1 

11.  25,07 

3.  14,76 

11.  25,57 

3.  21,56 

0.  25,66 

4.  16,05 

0.  26,16 

4.  22,85 

1.  26,30 

5.  17,39 

1.  26,79 

5.  24,18 

2.  25,59 

6.  17,34 

2.  26,06 

6.  24,12 

3.  26,28 

7.  18,74 

3.  26,76 

7.  25,51 

4.  26,98 

8.  20,13 

4.  27,45 

8.  26,90 

/br. 

5.  27,65 

9.  21,50 

read  • 

5.  28,12 

9.  28,28 

6.  28,28 

10.  22,83 

C).  28,77 

10.  29,62 

7.  27,49 

11.  22,71 

7.  27,99 

11.  29,50 

8.  28,06 

0.  24,01 

8.  28,57 

1.     0,79 

9.  28,62 

1.  25,24 

9.  29,14 

2.     2.05 

10.  29,18 

2.  26,50 

10.  29,70 

3.     3,31 

11.  29,76 

3.  27,77 

0.     0,28 

4.     4,59 

0.  28,99 

4.  27,67 

|  0.  29,50 

5.    4,48  _ 

for    2.  18,5 

read    2.  16,5     ' 

for    0°  4     3    2 

1    5                             read    0°  1    2    3 

4    5 

for    7,6 

read    7,5 

for    3,1 

read    3,8 

for    3,3 

read    3,1 

for    3,3 

read    2,9 

far    9,7 

read    8,5 

for    6,6 

read    5,6 

for    2,57582 

read    2,57562 

for    0°  4     3    2 

1     5                               read    0°  1     2     3 

4     5 

for    1976 

read    1970 

for    25 

read    26 

for    20 

read    19 

for    0,02250 

read    0,00250 

for    53,8 

read    53,3 

9.  18,3 
8.  1,0 
7.  5,3 
5.  18,1 
4.  0,8 
2.  13,6 


rend     +11.  57,7 

read    I'e'longation  eat  entre  9'  et  0' 

read    0.  4,53 

4.  23,8     ^i 

3.     6,6 

1.  19,3 

0.  23,7 
11.     6,4 


•ead 


9.  19,1 
8.  1,9 
7.  6,2 
5.  18,9 
4.  1,7 
2.  14,4* 


